"One odd afternoon" could have two meanings, depending on context. If you say "That was one odd afternoon!" it means that the afternoon was very unusual. If you say, "One odd afternoon, my friend, who I hadn't seen in years, called me" that would mean that the call was unexpected. The timing seemed random.

If someone is telling a story, they might use the phrase "one odd afternoon" which emphasizes that that day the event happened, since that afternoon was odd (weird) or not like the rest.