Have you tried cutting up pieces of veggies (and whatever) and mixing them in with the pureed foods? Or giving him the chunkier but still really soft Stage 3 baby foods? Or mashed (but not pureed) veggies, like potatoes, sweet potatoes, and avocados?
It seems like it could be a texture issue with him. If he eats cheerios, crackers, etc., maybe try giving him some crunchier foods, like apples, nuts, raw celery and carrot and see if he likes those. Just keep an eye out for choking with the carrots especially.
If he's still refusing that stuff, though, I'd say just keep giving him the pureed foods until he's ready. Still try to offer the other stuff, but don't push it, because the last thing you want is for eating to become a power struggle with him.
Good luck.