Recently I've been going to all the merchants in-game to try and find the Gloves of the pugilist which I think I must have sold. Anyway I get to winterhold and try Birna's Oddments to find Birna isn't there. I thought it strange so I wait and still nothing so I assume the worst and use the detect dead spell. I eventually find her corpse under the decking in front of the tavern (had to use raise zombie to get her out). Thing is I don't know how she died (dragon attack maybe?!) or how she got right under the decking or (and this is the important one) if there is anyway to search her shop inventory for the gloves? P.s. I'm on xbox so no dev. console.

Your best bet is to load a save from before she died. I'd say what is most likely to have killed her would be a dragon, so you don't remember any recent dragon attacks there?
She has a merchant chest, but if she purchased the Gloves from you, my guess would be that they'd be in her personal inventory - that is, her corpse.