Can Astigmatism Give You Wonky Eyes And If So Can It Be Fixed?

Astigmatism is only a particular variation of short or longsight so it can be fixed with glasses, contact lenses and increasingly by laser treatment, in normal ways.
Beyond the blurred vision from any refractive errror, astigmatism is only likely to casue the eyes to mis-align if it is so severe that one eye develops amblyopia (lazy eye), but this is true of any severe refractive error, particularly if only present in one eye. The amblyopia due to astigmatism, however does show unique features, such as better vision of single letters than a row of letters.
MIs-aligned eyes (cast, turn, strabismus) can be corrected in many cases, especially in young children.
In adults surgery to correct this is often cosmetic, and does not restore eyes to working binocularly, as a team.