how do you connect a stud wall to the underside of a sloped roof or stairs?

Cut wedges and use a pilot bit on a drill to go through the header and wedge. It helps from splitting the wedge. A good long enough screw should do the job. Hope that makes sense.

Forgive me if I misjudge the situation, but at the base of the stud wall you have a timber base or sole plate, each stud being fastened to it vertically, at the top, the surface is angled, but simple use of, ideally, a 6 foot spirit level and a bevel gauge to determine the angle from the vertical to the inclined surface; and then using the set bevel gauge it will be possible to cut the top of each vertical stud to exactly fit the head piece, which can be fastened with long screws to the base of the stair string, ideally set back the thickness of inset panelling (eg plasterboard or t@g cladding) or brought out flush with the stair string or adjacent wall and the joint can be covered with an appropriate bead or architrave.

Why wedge it? Surely better to use one piece of wood other than pieces

Angle cut your timber ends so they met the wall so your uprights can support your header, then you can start plug and screwing up, then finish buildering up your wall