None of them is incorrect, broadly speaking. You might hear any of those in informal speech, though the first one is the most common. The other two are likely to be hypercorrections based on the prescriptively correct option: "as soon as he saw that she and I were friends". Grammarians and English teachers will tell you to use the nominative pronouns in this sentence and to always put the first-person pronoun after other pronouns in a list. Some speakers misinterpret the rule and use the nominative only for first person, like in your second example. While I have the impression that can be a stable usage pattern, the third example sounds like a one-time thing to me, where the speaker is aiming for the prescriptive form but forgot the rule on pronoun order.
N'hésite pas à corriger mes erreurs.