My son's big toe nail has separated slightly from the skin and is smelly and oozing. The nail was quite bruise, but is now yellowish.

Fungus. Please call your PCP to make an appointment to be evaluated for fungal or bacterial infection.
See a surgeon. You are describing a bacterial infection under the nail. It needs to be treated by antibiotics and by drainage. A hole must be made through the nail to allow drainage, followed by soaks. Make an appointment for today.