I think that the Broadway production used a wig to enhance the "gussied up" appearance of Annie to look like the cartoon character, with the curly hair and trademark red dress...Andrea's own hair seemed to be a regular 70's style but dyed red, darker at the start of the run, lighter later on. Beginning with Shelley, and also Sarah J, Annie's "regular" hair was more of a short red dutchboy, then a bob for Allison and Alyson. It also appeared that there were two wigs, one with floppier curls, one with shorter, tighter curls.
As for Aileen, I read that she had to have a wig because her own hair was dark brown and wouldn't look realistic?? That doesn't make sense to me really, because couldn't they bleach it, then dye it redddish and perm it ? I think they had to bleach her own hair anyhow because of the dark color showing through the wig. I think Jon Merrill has addressed this question...I thought the transition for Aileen was more realistic than in the show, but everything else in the film..NOT !