This is an interesting one, isn't it?
Via certainly works, so isn't likely to cause any raised eyebrows. On the other hand, you point out that oil is transported
in tankers, and the tankers, in turn, can be said to be floating
on the river - therefore by extension, you could say the oil is transported
on the river. Those who follow the advice to choose the Saxon over the Latin may well opt for
on anyhow
Siggy