Meaning

verb to move in a twisting or contorted motion, (especially when struggling)

verb cause (a plastic object) to assume a crooked or angular form

verb turn in the opposite direction

originThe sense "intertwined" comes from twist (verb) by the late 15th century. The sense "mentally disturbed, perverted" is probably from twist (“mental peculiarity, perversion”, noun), which is attested by 1811.

Etymology from Wiktionary, CC BY-SA 3.0