If there's no velocity, those impulses are presumably going to be zero. Most game physics engines depend on solving contact impulses to resist penetration by clipping the penetration velocity to zero.
I don't know what your application is, but it sort of sounds like you want to estimate the force based on the depth and normals of the contact points, plus some 'spring rate' that you provide. It's going to be highly imperfect, since you'll only be getting the 4 "best" contact points from Bullet. But if that's the way you need to go, then the force vector would equal spring_rate*depth*normal, and you'd apply it at the point of contact.