He was subpoenaed, and he is testifying in a deposition, so he is indeed under oath.
https://judiciary.house.gov/wp-content/uploads/2018/06/062218_Strzok-Subpoena.pdf
From the American Bar Association, https://www.americanbar.org/groups/public_education/resources/law_related_education_network/how_courts_work/discovery.html :
One of the most common methods of discovery is to take depositions. A deposition is an out-of-court statement given under oath by any person involved in the case. It is to be used at trial or in preparation for trial. It may be in the form of a written transcript, a videotape, or both. In most states, either of the parties may take the deposition of the other party, or of any other witness. Both sides have the right to be present during oral depositions.
Depositions enable a party to know in advance what a witness will say at the trial. Depositions can also be taken to obtain the testimony of important witnesses who can’t appear during the trial. In that case, they’re read into evidence at the trial.
Often a witness's deposition will be taken by the opposing side and used to discredit the witness's testimony at trial if the trial testimony varies from the testimony taken during the deposition. (A lawyer might ask a witness at trial, “Are you lying now or were you lying then?”)
Usually depositions consist of an oral examination, followed by cross-examination by the opposing side. In addition to taking depositions, either party may submit written questions, called interrogatories , to the other party and require that they be answered in writing under oath. If one party chooses to use an interrogatory, written questions are sent to the lawyer representing the other side, and that party has a period of time in which to answer.