At work I use a so-called "Mavic Hub Oil", but not really sure exactly what it is. It's similar viscosity to a wet chain lube, so anything similar will be OK.
To service the hub, pull the left side axle end-cap off (it'll be firm but will just pull out with a bit of effort) & insert a 10mm allen key into the open axle end, and a 5mm allen key into the right end. Unscrew the right-hand axle end cap. You'll then be able to pull the freewheel body off. Be really careful when you do so, because the pawls are liable to fly off & lose their springs once they're freed from the restraint of the body.
Check the main bearings (there will be two in the hub body and one in the freewheel body) are running smoothly & replace if necessary. These are standard sizes, so you can get them at your Local Bearing Shop. Clean all the bits & reassemble with a light coating of oil - you don't need lots, just a drop on each of the pawls & a smear on the rubber seal on the hub body. There's a small washer that acts as a spacer between the right side hub body bearing and the freewheel body bearing - make sure you don't forget to put that back in, otherwise it'll bind up & behave worse than it is now! Bung a little bit of grease on the thread of the right-side axle end before you screw that back in.