How clean inside range hood, over fans?
I would start out by thoroughly cleaning the fan housing and blades. Most of the grease you're referring to will be on the blades and will really cut down on their efficiency. So remove that grease and you'll see a big difference. Anything more than that will require removing the hood.
If you have access to the area above the hood, like a cabinet or attic, you can disassemble the vent pipes and clean them. Just make sure to re assemble them correctly.