If you get stiffer mounts, the engine vibration will transmit through the body more. Stiffer mounts, more vibration. If you don't absorb vibration, it gets transmitted.

Strut bars keep the strut towers from flexing independently of each other, so they're tied together and more rigid. Steering tends to feel less vague and the front end feels more predictable and planted. Sway bars add a torsion spring between the left and right wheels, decreasing the amount of travel each wheel can have in relation to the other, therefore lowering body roll.