Some imperial measurements are pretty random (1 mile = 1720 yards, 1 yard = 3 feet?), but many of the commonly used ones are just based on fractions or convenient values instead of everything being base 10.
Maybe this will help with the fluids. Looking at a table of fluid measurements, it is easy to see it is just a base 2 system.
2^-1 oz = .5 oz = 1 tablespoon
2^0 oz = 1 oz = 1 oz (2 tablespoons)
2^1 oz = 2 oz = 1/4 cup (4 tablespoons)
2^2 oz = 4 oz = 1/2 cup (8 tablespoons)
2^3 oz = 8 oz = 1 cup (16 tablespoons)
2^4 oz = 16 oz = 1 pint (2 cups)
2^5 oz = 32 oz = 1 quart (4 cups)
2^6 oz = 62 oz = 1/2 gallon (8 cups)
2^7 oz = 128oz = 1 gallon (16 cups)
I think it is quite beautiful in a way. That doesn't explain why we have 12 oz beers though.
Coming from a country that uses litres and millilitres, European centilitre paper cups just look plain weird. It's certainly the most appropriate unit for the task, but I'm just not used to it.
I still don't get cups or the fluid measurements though, except that 12 oz a beer bottle and 16 oz is a medium soda bottle (medium in European terms).