Beverages at the store: 2 pints of milk; 2 quarts of orange juice; 16 cups of chocolate milk; and 32 fluid ounces of lemonade.

First, we need to convert all the measurements to gallons so that we can add them together:

- 2 pints of milk = 1/2 gallon
- 2 quarts of orange juice = 1/2 gallon
- 16 cups of chocolate milk = 1 gallon
- 32 fluid ounces of lemonade = 1/4 gallon

Now we can add them up:

- 2 containers of milk = 1 gallon
- 2 containers of orange juice = 1 gallon
- 2 containers of chocolate milk = 2 gallons
- 2 containers of lemonade = 1/2 gallon

Total = 5.5 gallons

So Julius bought 5.5 gallons of beverages.