I always have problems with my legs after a couple of cocktails too..
Seriously, it's not uncommon for cockatiels to stand on one leg.
Sometimes they'll panic at night, maybe sprain a foot or a leg and then you'll notice they won't stand on it for a couple of days. This happens, it isn't all the common, but I've seen it a couple of times on my birds.
However, what you are describing (assuming your description is accurate) is something more than a sprain. If you are saying that your bird cannot stand on both legs, and that you can visually detect a difference in one leg from the other, I'd take him to a vet that works with birds. You could wait a couple of days and see if there is any change for the better, but that is up to you. If the bird is in any discomfort, I'd go sooner rather than later.
Bob