The titles of the paintings are all mathematical references (isometry, inverse curve, parabola, postulates, arguments, etc).
Sokolov is rather secretive about the tools he uses to create his paintings, even leaving Bunting, an art dealer, in the dark as to the medium he paints on.
If Corvo drinks the cider sitting on the table by Thaddeus Campbell before going to meet the Empress at Dunwall Tower in Returning Home, the painting "The Isometry of High Overseer Thaddeus Campbell" will reflect that and the table will be empty. Sokolov will comment on Corvo's action, saying that he needed it to draw attention away from Campbell.
In The Knife of Dunwall and Dishonored 2, the painting can be found with the cider decanter present, meaning Corvo canonically left it there.
In The Knife of Dunwall this painting with the decanter present, or the reflection of it, can be found in the Void. It cannot be taken.
The painting "The Spymaster's Axis of Asymmetry" will always be found in the bedroom of the targeted Lady Boyle and thus can change location from one playthrough to another.
The last portrait in Dishonored will be inaccessible unless at least one of the side missions for both Granny Rags and Slackjaw has been completed.
Duchess Callas Abele commissioned the painting "Radanis Abele's Incongruence with Time" from Sokolov, as a tribute to her deceased son. The painting might have been lost among her collection of artwork when her second son, the new Duke Luca Abele, rebuilt the Grand Palace.
Sokolov's portrait of Jessamine Kaldwin, "The Empress and the Empty Set", can be found in Dishonored 2 in the throne room of Dunwall Tower, but not collected, during the mission A Long Day in Dunwall. The portrait appears again, although vandalized this time, outside Ashworth's office during the mission The Royal Conservatory. This mission also happens to take place after the return of the Duke to Karnaca.
Collecting all of Sokolov's paintings in Dishonored will unlock the Art Dealer achievement. The equivalent of this achievement in Dishonored 2 is Art Collector, although this includes collecting Delilah's paintings as well.
Sokolov was once painting a picture of a beautiful young woman. She died before the painting was finished, so he burned it.
When Sokolov painted "Vera Moray and the Affix of Her Skin", he was no older than 24.
Sokolov displays considerable annoyance at being forced to paint Campbell, viewing it as an insult to his own genius.
If Billie Lurk steals the "The Outsider in Conditional Dreams" from the Albarca Baths, it will be in the Dreadful Wale's cargo hold at the beginning of the mission Follow the Ink. Inspecting it will begin a short conversation between Billie and Daud.
Although the Outsider claims at his shrine in The Royal Physician that he has never visited Sokolov, two of the latter's paintings can be found (one in Dishonored, one in its sequel) depicting the Outsider with a large degree of accuracy. How Sokolov attained such accuracy is unknown, although it's possible he asked someone such as Daud, whose portrait he also painted some years ago.
"The Isometry of High Overseer Thaddeus Campbell", beside appearing two times in Dishonored main storyline, and one in Dishonored 2, is encountered by Daud in The Knife of Dunwall. In addition to that, in the novel Dishonored: The Return of Daud, upon visiting Maximillian Norcross' house, Daud happens upon the portrait of the High Overseer Campbell. As there are no other known portraits of this man, it is possble that Norcross holds in his collection the ill-fated Sokolov painting, some weeks before it can be found in Karnaca docks.
The very night Daud visits the mansion, it is robbed by the Eyeless gang, eventually bound to Karnaca. The thiefs may have stolen the painting along with the Twin-bladed Knife that was their primary target.
"The Outsider in Conditional Dreams" is owned by the Eyeless operating the fighting club in Albarca Baths a couple of months after the portrait can be found by Emily in Campo Seta Dockyards. Afterwards it is taken by either Billie Lurk or Daud and held in the Dreadful Wale cargo hold. It is unknown, however, if was sold shortly after or burned along with the ship.
Aramis Stilton is known to have bought a Sokolov painting at a flea market at a ridiculously low price.