get drunk, feel sick, poisoned, elated, spellbound
醉 centers on intoxication: the physical state of being drunk or poisoned, and the mental state of being elated or spellbound. The meanings connect through the idea of being overwhelmed by a substance or feeling.
醉 combines 酉 (alcohol vessel) with 卒, which likely contributes the sound and may suggest the idea of finishing or ending, as in reaching the end of sobriety. The exact role of 卒 is uncertain.
The alcohol radical 酉 on the left and 卒 on the right suggest a soldier (卒 can mean soldier) who has had too much to drink from the wine vessel. He is now drunk and spellbound.
For スイ, imagine a drunk person swaying and saying 'swee' instead of 'sweet': swee -> スイ, as the alcohol takes effect.