What do you consider to be 'odd'?
I have a small (but growing) collection of souvenirs from the 1904 St. Louis Worlds Fair. My grandparents met there. I have glassware, plates and little metal trays, 105 year old magazines with articles about the Fair, lots of post cards and stereoview picture cards. The blank post cards are more valuable but I like the ones that people have written on. It's like seeing a little slice of someone's life from 105 years ago. My favorite thing is a fancy little aluminum case with three slots in it that opens like an egg carton - men put their cigars in there and then put the case in their shirt pocket - neat! Nobody can ever figure out what it is!
I also have a ton of old antique glassware, lots of Victorian stuff, EAPG, some just old weird things. I started buying old glass candy dishes, then branched out to wine glasses (mostly Tiffin) and decanters, sugar bowls and spooners. THEN I got in to old Victorian pitchers and Depression glass stuff and a few pieces of Carnival glass. When I ran out of shelf space, I built more shelves, but now I'm kind of maxed out again.