When you are dealing with a period that is this remote, you're also dealing with one for which there are at best fragmentary sources, many of which are late – the Anglo-Saxon Chronicle, for instance, while it certainly does cover Oswy and his reign, was not set down in writing until the end of the ninth century, so it will always be uncertain how accurate what it says about the middle of the seventh actually is.

To address the specifics of your question, though, and while there's always more to say, you might like to check out an earlier response I wrote to what's substantially the same query; I note with apologies that the subsequent deletion of the account of the user who posted the original question has stripped out some of the question itself, which now exists only as a stark title, but it originally asked something along the lines of how Oswy could have been married to Fín when he is known to have had other wives.

In the specific context of your question, you'll note that the main controversy is not whether Oswy had a "liaison" with Fín, which tends, in the absence of evidence to the contrary, to be accepted by historians of this period, but whether the relationship occurred in the 650s as Wiki has it or much earlier, in about 630, and whether it should be considered a marriage:

How did King Oswiu of Northimbria marry Fín, an Irish princess?