How did Mormon missionaries around 1900 understand and act against Satan and his incorporeal minions? The diaries point mostly to literal belief in sentient, personal beings that actively worked against the Elders by influencing understandings and feelings.  There are a few acknowledgments of the possibility of possession, but no instances of it. In three cases the Elders report the direct detection of evil spirits (rather than deducing influence from the unreceptiveness of the people) but there are no mentions of exorcism: these Elders resisted Satan by living gospel principles and persuading others to do the same.
Some mentions of Satan were probably meant as ?just an expression? but with an undercurrent of doctrinal seriousness.  For example: ?after meeting was over the kind people or the Poor people that is the Poor devils all went home and went in their good beds but left us to Sleep on the Benches in the School house.? 
Elder Clark provides a more ambiguous usage with ?had a devil in him?:
we meet one family who we could See the devil Sticking out of him before we got to the house and when we got there I told him our business and the man Said all the Preachers had ought to be killed and was very excited but when he had Said his Say then I laid the gospel of Christ before them and got them cooled down and they had to Say that was Bible then we go on again and left them feeling good. 
At face value the phrase suggests literal ?possession? but, in context, seems to be an idiom meaning, ?was very upset.? Based on Clark?s other mentions of devils, I think an acceptable gloss would be, ?had his heart stirred up to anger by Satan? 
Literal Beings Stirring-up Hearts
Satan appears most often in the diaries as an instigator of apathy and/or conflict.  Again, Elder Clark:
we found the people more bitter we was ordered outside their lots 4 times about 5 times the people would Slam their doors in our faces the devil had been there while we Slept and had Sown tares among them. 
Sometimes the missionaries asserted a stronger connection between human and spirit: ?While in the store one of Satan?s votaries came in and jumped on us for an argument.?  Nowhere do I find an implication of ?Satanism?: to oppose Mormons was to serve Satan or fall under his sway. The Elders resisted Satan with unity and right-living, for ??it is by united action, only, that the servants of the Lord can prevail over the powers of Satan.? 
Literal Beings Detectable by Third-Parties
Only four entries suggest consciously detectable Satanic power. Of a 1902 meeting, Jones wrote, ?It was very hard for us to sing and talk, as it seemed like there was an opposing spirit in our midst.? The next night
The same opposing spirit that was against us the night before was present again. I spoke for 55 minutes upon Authority, but it seemed like I could not branch out. After closing, Satan arose in the form of a Campbellite man and wanted to show us wherein we were wrong. Made several assertions that he could not prove. We did not answer him as enough had been said. 
Elder Duffin (not yet President) recorded a similar instance.
As soon as we left Hutchins today a feeling of depression took possession of us; later we saw the reason of it. When we got to the Hunter settlement, we found the powers of evil had been at work and had nearly destroyed the faith of these people in the work of the Lord. He had been circulating all manner of false reports, and had also tried to deceive the people by turning the scriptures from their rightful meaning. But by the power of God we were enabled to get control of these evil spirits, and to establish the truth and faith again where there had been doubt. 
Later, Duffin wrote of a Holiness manifestation, ?I did not question but what she had the spirit but thought it was of the devil,? which he dealt with by getting her ?out of the room? and speaking ?a few words to quiet the feelings of the people.? 
In all four cases, the Elders resisted evil spirits by teaching and persuading. 
The ?Southwestern States Mission? series uses the diaries of six missionaries who served in eastern Texas around 1900 to illustrate aspects of Mormon material culture, lived religion, and social History. The missionaries are Mission President Duffin and Elders Brooks, Clark, Folkman, Forsha, and Jones. The series is inspired by Ardis Parshall?s serial posting of the missionary diary of Willard Larson Jones at Keepapitchinin. Previous installment here.
The footnotes are even longer than usual. Let’s call them the “SC Taysom Memorial Footnotes.”
 Insert here all the usual caveats about the small sample size. Note, also, that almost all the citations come from two Elders, Duffin and Clark. Jones makes a much smaller but still significant contribution. Brooks, Folkman, and Forsha hardly mention demons at all. Furthermore, Duffin and Clark were both in their forties, compared to early-twenties for the others, so there might be an age or generation factor .
 See also, ?Heathen.?
 Clark, 1901 Jun 17 Mon; ??said he I don’t want to hear nothing from you?and said there was the gate So we leave the devil and go to the next house? (Clark, 1901 Sep 03 Tue). When asked about anti-Mormon literature: ?you can get them at the devils headquarters? (Clark, 1901 Jul 25 Thu). Apostle Abraham O Woodruff told missionaries to ?avoid wine and women as you would avoid the gates of hell? (Duffin, 1902 Nov 17 Mon). To a man who asked them to prove faith by drinking a poison: ?[we] told him that we were no fools and said to him that he was in the same condition as old Satan when he tried to get the Savior to give him a sign. He says, ?I am the devil then, am I?? ?Yes, sir,? was the reply.? (Jones, 1902 Jan 26 Sun).
 Clark, 1900 Jul 25 Wed; ?one man who had a devil in him and told us he didn’t want anything to do with us and Said he had all the religion he wanted? (Clark, 1900 Jun 29 Fri); ??found one man who was So filled with the devil he wouldn’t ask us in or take a pamphlet? (Clark, 1901 Jan 09 Wed); ??when we go to a house and was going to ask for lodgings when I See the devil was in him instead of asking him I offered him a pamphlet? (Clark, 1901 Jun 29 Sat)
 Book of Mormon-style language at no extra charge. Elder Jones used a similar idea: ?We tried to reason with him but he was so full of the spirit of the evil one that we could do nothing with him? (Jones, 1902 Jan 03 Fri).
 This undetectable, conflict-engendering “devil” could be read as a merely figurative personification of generic human traits, but I find nothing that demands such a reading. And there is other evidence of literal belief. Of one interrogator Elder Jones lists the statement that ?Satan and his angels fell after the flood? as one of several ?foolish ideas?we refuted as fast as he would advance them? (Jones, 1901 Dec 14 Sat). One ?old crabby man? told Elder Jones ?that he would rather hear the devil preach in his house than a Mormon,? of which Jones noted, ?Of course the poor ignorant fellow did not know his conditions? (Jones, 1901 Jun 12 Wed). By taking the timeline and hyperbole at face value, Jones reveals his own belief in a literal Satan.
As an aside, and turning the tables? another Elder was at a Methodist revival and ?they [preachers] asked one of Bro. Cude’s boys if he wanted to go to Hell or Heaven and he told them to hell.? (Folkman, 1901 Jul 15 Mon).
 Clark, 1901 Jun 18 Tue; the imagery is loosely based on the parables of the Sower and/or the Wheat and Tares. ?…we found that the Evil One had been there in the meantime and had poisoned his mind.? (Duffin, 1900 Jan 08 Mon); ?In the evening came to Mrs Shults, who treated us very cool and said that she was expecting company and hence could not keep us. How quickly the evil one has taken the good seed out of her heart.? (Duffin, 1899 Oct 28 Sat); ??and said many other things that was false thus you See we had Sown good Seeds and the devil came a long and Sown tares among the good Seed fulfilling Scripture for the man whom we Stayed with wouldn’t take a pamphlet.? (Clark, 1901 Oct 12 Sat); ?…find them mostly indifferent Some would receive a pamphlet while others would not the devil had been working among them and had got them prejudice against us? (Clark, 1901 Aug 27 Tue); ?find Some people Bitter towards us the devil have been around ahead of us? (Clark, 1900 Jul 12 Thu);
Satan also got blamed for… backslid members: ??one of the Coil girls came over and said she wanted her name taken off from the books. I regret to see a person taking a back step but the evil one is watching for such places.? (Jones, 1900 Aug 29 Wed); contention in the branches: ?It seems that Satan is determined that the people who live in this land shall not be united? (Duffin, 1904 Jul 31 Sun); a companion?s resentment: ?he] had given way to the temptations of the evil one? (Jones, 1901 Mar 14 Thu ); potential violence: ? The evil one had aroused the people till they had made threats that they were going to mob us? (Jones, 1900 Aug 12 Sun); and confessed malingering: ?[he] has seen where the power of the evil one was leading him?? (Duffin, 1899 Nov 13 Mon).
 Jones, 1901 Dec 31 Tue; ?After meeting one of Satan?s imps came up and asked him [Duffin] a few questions but it was not long before he went away a-roaring? (Jones, 1901 Dec 01 Sun); ?Went on and met another hard headed Baptist that wouldn?t have anything to do with us. … The Baptist he said was the Church of Christ. I think he was serving the devil more than anything else? (Brooks, 1900 Sep 27 Thu).
 Duffin (at this point, President), in a letter to all missionaries (Duffin, 1904 Aug 13 Sat).
 Jones, 1902 Jan 16 Thu – 17 Fri
 Duffin, 1900 Jan 30 Tue.
 Duffin, 1904 Jul 10 Sun. As a traveling Elder, Duffin spoke of his homesick companion as having ?been almost possessed, if not quite by an evil spirit.? (Duffin, 1899 Nov 13 Mon). The Elders didn?t just associate the Holiness with Satan: Elder Jones and some companions visited a Catholic Church ?and listened to them carry on in their hellish way for two hours? (Jones, 1901 Sep 08 Sun).
 I read Duffin?s statement that, ?by the power of God we were enabled to get control of these evil spirits,? as ?God enhanced our powers of instruction and persuasion? rather than ?we formally exorcized the demons and then taught like we would normally teach.? If he had intended the second reading, I?m pretty sure Duffin would have phrased the description more clearly.