You basically have to play much more carefully and defensively. You characters have a hard time against Honda, but, except maybe for Cammy, they aren’t as bad as a lot of people believe.
With Blanka, neutral jump LK is great at stuffing most of Honda’s attacks. Bore him to death to force him to take initiative, make him lose life trying to get past that n.j.LK. Doing a LK after you land from that is pretty safe too. If you see him walking forward too close, then that’s when crossup LKs are most useful. Otherwise try to avoid jumping at him, you’ll just get headbutted. Max range j.HK is pretty safe too, will stuff headbutts if timed correctly IIRC. Slide and cr.HP are good, relatively safe pokes.
Against careless headbutts, jump over him and then do j.LK, cl.MP, HK or j.LK, cl.MPx2, cr.HP if you have the execution for it (this one will almost guarantee you a dizzy).
Don’t try to do many Blanka ball shenanigans like ball into throw or you’ll get thrown. Corner ball crossups can be useful every now and then though.
For Dictator, you should also try a defensive approach. Get back (don’t corner yourself though) and wait for him. If he gets too headbutt happy, you can jump to avoid it and come down on him with a big combo into knockdown. He doesn’t have good answers for crossups, so you can get the match with an ambiguous crossup into ToD afterwards. Headstomp is a relatively safe to deal chip damage; if you can, do some to get a life lead and then turtle to make him come at you. Badly timed hands can be punished with Psycho Crusher, and you can then try to ToD afterwards.
If you use Psycho Crusher to counter headbutts, only use LP Crusher, as it has much more priority.
As for Hawk, the strategy is simple, yet very difficult to execute. Turtle him doing repeated cr.LPs (stuff headbutts and Hands), force a knockdown (with dive, cr.HK or DP) and then do the safe jump option select loop. Not even Honda can escape it.
Low hitting dives can’t be punished with HP headbutt. You can try to trick Honda into punishing a low blocked dive with that, counter him with DP and start the loop. If he gets hit by a cr.LP, you can try to catch him off guard with a walk up throw as he comes down something to use sparingly of course).