His current batty appearance aside, Morbius's powers have consistently been super strength, quick speed, enhanced senses, his fangs, and his claws. We've actually seen a lot of his very recent appearances really use his claws, which have been shown to sheer metal.
His "flight" is also a consistent power, as well as his hypnosis, but how they're portrayed changes dramatically from writer to writer.
Morbius can fly/glide because he has hollow bones, like a bird. It should be noted that real bays do not have hollow bones, just adorably small and delicate ones. Some writers have also attributed his gliding to some sort of psychic ability that allows him to better detect and control air currents. This sort of goes into his hypnosis, which has been portrayed as anything from just being a bit persuasive to full blown mind control.
Really, how these powers are used really depends on the writer and what they want with Morbius.