The density of the oil does matter. Let me try to be the teacher that I am and, rather than giving you the answer, ask you some questions that might get you on the right path. First, I will say that figuring out the mechanical input power is correct as one of the first steps. Now for some questions:
1) What do you know about mass flow rate? (Are you familiar with the mass flow rate equation?) If so you can solve for an another important input state variable.
2) You are also given the total pressure increase from the input to the output. Do you think the level-flow form of the Bernoulli's equation might help you get from input to output once you know the input state variable from (1)?
3) Wouldn't the output power = output force * output velocity?
I hope I haven't made it TOO easy!