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Mixed bag - lots won't do reservations as they're small trains without a bike bit to put it in, so there is no space to reserve. Used to commute that route and it was different every day - I'd say you'll probably be ok, but wouldn't guarentee it.
Alternative - either the X90 or Oxford Tube coaches, both departing from the coach station in the center of town take bikes, are cheap, and pleasant (big coaches, wifi etc). Take about 90 minutes.
How easy is it to get an afternoon train from Oxford to London with bike, like 4pm? Every single advance service I look up on the FGW website says "no bike reservations available".
Customer service by phone/tw were no help at all ("try your luck with staff on the platform btw no refunds for advance tickets").