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Pullets, in show terms, are female chickens or other poultry under a year of age. Easter Eggers are mixed breed chickens, so you wouldn't be able to show them at open poultry shows. You might, however, be able to show your Easter Eggers at county or 4-H fairs in a crossbred, pet, or egg layer class.
Purebred Rhode Island Reds can definitely be shown. Keep in mind, though, that it is hard to have competitive Rhode Island Reds unless you get them from a breeder. Hatchery Rhode Island Reds are better called "Production Reds," since they are great layers, but aren't bred to be show quality in color or body type.
As for whether you can show your "Browns," it depends on what breed they actually resemble. If they're mixed breeds (as many "Browns/Reds" are), then you could only show them in a production class. If your Browns happen to be a recognized breed of chicken, like New Hampshire, then you could show them in their breed class.
If you post some photos of your chickens, other members and I will be happy to look at them and tell you how show quality they are.
