Oliver is a biochemist who, prior to his kidnapping by the AM, worked for the U.S. Department of Defense. He was fired and subsequently taken by the AM after an incident at work in which "there was a woman involved, passions were inflamed" and he ended up accidentally making a bomb with his ability. Although he was able to defuse it before people were hurt, the incident did not go unnoticed and led to his incarceration by the AM for three years up until Sam, Joan, and Owen began their tier 5 clear out.
After the events of The AM Archives, Oliver travelled across Europe and Asia doing work for The Order, specifically in working with atypical artifacts for three years until his return to Boston in The College Tapes.
Oliver's ability is transmutation (also referred to as alchemy). If given some of the base elements, he can alter states of matter.
(Please note this section contains minor spoilers for The AM Archives.)
Mark and Oliver met in The AM Archives during Helen's break out. Oliver helped to recreate Dr. Sharpe's serum, which was used to keep Alex from flaring up and causing a fire as well as helped incapacitate Helen. Oliver used samples of Mark's blood in order to recreate the serum. Mark encouraged Oliver during this, trying to reassure him and help him focus. At the end of the series, Oliver and Mark seem to forming a tentative friendship, with them both expressing a desire to spend more time with someone who understands their experiences from being on Tier 5.
In The College Tapes, Oliver and Caleb start off as strangers. The extent of their knowledge on each other is limited to what Mark and Joan had told them, with Joan having lent Caleb and Adam Oliver's research. They first meet in Non Facias Malum after Oliver had trapped accidentally Caleb and Adam with him in a time loop in Yale's Russel Library.
In the next episode, Librum De Spiritum, we learn that Caleb got Oliver's number from Mark (under the false pretense that he had questions about his notes). Caleb then meets with Oliver in a lighthouse to discuss and examine the book. They explore how Caleb's ability interacts with the book and listen to its entries.
Oliver first hears of Beck in Librium de Spiritum when the book presents him with an argument between him and Blackwell. Upon hearing that Adam also knows of him, Oliver insists they go to meet him. Mark talks him into visiting the next day where they break into his office with the help of Caitlin. Oliver is already suspicious of Beck due to what the book showed him but the man's understanding of Caleb's bonkers explanation and the general situation only seems to feed it. After Oliver's runs off with the book when Beck storms out, the two don't meet again until The College Tapes Episode 14. When they do, their relationship is tense with Oliver accusing Beck of snooping in his memories and trying to take down other atypicals. Beck corrects him, explaining that he was actually trying to stop Blackwell from making atypicals out of regular people. Due to the high emotion Oliver begins to feel regarding tier 5, Beck, and subsequently Mark, accidentally sees a snippet of his time there. Oliver runs off upon the realization of what they both saw with Mark going after him. The two don't interact much after that, although Oliver expresses being bitter over how much time Mark has been spending with Beck.
Not much is known about Sam and Oliver's relationship post-TAMA. It is revealed in Malus Denarius, however, that Sam funded Oliver's three year expedition across Europe and Asia.