That would depend on the users race! In both Undertale and Deltarune, a MONSTER can only absorb a HUMAN SOUL, and a HUMAN can only absorb a MONSTER SOUL. However, I'm not sure how that would work for other races out of their universes.
As for what happens, that depends on how many SOULS you absorb. Absorbing 1 or 2 will simply change your physical appearance, with the form of a MONSTER being dominant for the absorption. You'll also gain similar physical features to who you absorb, mixing in with your own form. 3-5 will net some distinguishing features of angelic nature or demonic nature based on the host's affinity, although a angelic absorption CAN be evil and impure. Appearances aren't everything. And the last two SOULS will net you both the power and semi-appearance of a God.
However, do be warned, as there are 2 main caveats! The described absorption features apply to MONSTERS absorbing HUMAN SOULS. If you were to absorb the SOUL of a MONSTER, you would need to absorb every MONSTER SOUL in the entire UNDERGROUND just to equal one human worth of SOUL power. Not only that, consciousness will be shared between all SOULS inhabiting said host body. So I suggest only absorbing SOULS that are truly pure.
I am neither monster nor human, so I don't know how it would work for me. Considering the caveats, however, it may be best for me to steer clear of absorbing souls.