How exactly would you describe someone being hit by force damage? For example, if someone was hit by fire damage, they might be burned, or slashing damage, they might get a few cuts. So, how would force damage be described? 

They would get a few bruises, and they may feel a bit... Tingly. Just imagine how someone would feel if they got hit by someone casting "Stupify" on them

Think of it kind of like arcana, the in-between of psionic (Psychic), holy (Radiant), and death (Necrotic). It isn't particularly hurting the mind, raining down radiant fire, or draining the life force. It is just there, and a energy of pure magic sent for destruction, like a weapon, but a weapon made with spells, and of pure magic. Like a corner Mystra's weave torn of, unchanged yet reshaped. Made the same way yet in a different form, and flying through or slashing, like a bullet or knife. As StereotypicalDM said, it would feel tingly; but it would also hurt, not targeting the only soul, only the body, or only the lifeforce, but all at once, like a weapon tearing your mind and body, all at once.

 A feeling of claustrophobia as their being crushed,  a squeezing sensation, a blow that bruises the skin.