"pressed solid oak" is not meaningful. You don't buy "pressed solid oak" at the lumberyard and you don't make such a thing in the shop. I don't know what he could be referring to.

I'm not a stair builder, but MDF does seem like an unlikely choice for stringers. It's a fine material for certain applications, but stringers require some tensile strength that I doubt MDF can provide. I did a search on a professional woodworking forum for "MDF stringer" and got no relevant hits.

Having said all of that, the picture looks nice. He could be a fine stair builder and a lousy communicator.

Ok here is some clarification. Does this make sense?

Components to staircase-
The stringers are made of layers of plywood, regular plywood in the core and veneer plywood for the outer visible surfaces.
The risers would be made of either 1/2" veneered particle board or 1/2" veneered plywood depending on availability of species of wood chosen.
the treads will be solid hardwood and so will the trim.

Much better. I wouldn't have any problem with plywood stringers. I'd rather avoid particleboard risers, but I'd be fine with plywood there, too. Solid makes sense for the treads, since a veneer there would soon be worn through.