Well, if you think of gravity as an effect of the curvature of spacetime, it's really best not to think of it as a force anymore. Instead, it's better to think of the attraction of gravity as the effect of spacetime curvature on the trajectory of an object. For example, instead of thinking about the sun pulling on the Earth to keep it in orbit, you can think of the sun as warping the spacetime around it. As the Earth moves through this warped spacetime, it ends up traveling on a curved path.

Now, I'm not quite sure what you mean by an "omni-directional" force; certainly, any object moving in a curved spacetime will have its trajectory affected by this curvature. In particular, this curvature doesn't only affect the center of mass of an object; it affects the entire body of an extended object. Does this answer your