Nearest Wal-Mart is probably the one on Hwy 192 east. They have food there (Super Wal-Mart) which includes beer and wine, but I'm not sure about hard liquor.
From Disney (OKW), follow Epcot Center Drive (check the map they give you at checkin). This becomes route 536 after it leave Disney property. Go about a mile to route 535, turn right. Then go about another mile or so to route 192, turn left. The Wal-mart is a couple of miles on the right.
If you're staying at Boardwalk or VWL, it's easier to take World Drive directly to hwy 192. Go east 5-6 miles to the Wal-mart.