Seven attacks + Road Roller
Khan can only learn seven moves? An Anubis character can learn an entire character's move set. Chaka has a super demonstrating this functionality. Additionally there are icons to show learning 1, 5 and 10 attacks and the like.
[Not sure what I was thinking - for some reason I thought no more icons showed at 7. Ha. - Chaka's super is special (as in stupid) anyways - since he forgets moves learned previous to it after he gets hit -- Fayk] Additionally, yes, the first hit of the road roller is classified as physical attack, and as such can be learned.
This shows learned icon 10, 5, 1 and 1 respectively and learning the road roller. Moves learned, were: A, 2A, B, 2B, C, 2C, j.A, j.C, 236+A, 236+S, s.A, s.2A, s.B, s.2B, s.C, s.2C, Road Roller.
I didn't bother with the jumping stand attacks or the follow-up for s.214+A/B/C, nor did I try countering his blockable command throw. This means that Dio has around 20 learnable attacks in total, assuming dashing variants are not classified as different attacks.
[ Additional -- Thanks for the fact-checking -Fayk]