Eggy would probably be from earth-bender, maybe an air-bender, either way he could be the Avatar potentially considering the whole "chosen one" kind of thing he has going on.
Same applies to the other Eggyhead versions, as well as Essy.
Omeletta and Ove could be fire-benders or water-benders, depends on the day.
Blaze's powers basically are fire-bending, but his personality is a lot more like that of a water-bender.
Reality Empress 401 is fire-bending, without a shadow of a doubt. She's maniacal and extremely violent. She'd literally just be Azula at that point.
Ribeye would not be a bender. He would be the cabbages guy.