Why is propanediol soluble in water?
This question requires some additional specification before it can be answered.

Propanediol is ambiguous as a chemical name. There is 1,2-propanediol and 1,3-propanediol, and these are different compounds (namely, structural isomers).

Though either way, if you check references, you will see that both compounds are miscible with water, so the solubility is infinite.

See: 1,2-propanediol and 1,3-propanediol.

The term "oil" simply refers to the fact that it is a viscous liquid at room temperature.

Unfortunately, generalized solubility is hard to determine. 1,2-propanediol appears to be miscible in several different polar solvents, so you might be able to dissolve in something anhydrous.