What is the definition of mountainous area? MEA, MORA, grid MORA, and MOCA for a non-mountainous area gives 1,000 ft clearance from the highest obstacle, and in mountainous area gives 2,000 ft clearance from the highest obstacle. 

But what is the exact definition of a mountainous area?

I have also heard that MOCAs have a different clearance calculation for the mountainous area depending on the terrain/obstacle elevation, (3000 ft - 5000 ft gets 1500 ft clearance) and (above 5000 ft gets 2000 ft clearance) can someone clarify this.
(I'm assuming you're asking about the USA.)

14 CFR 91.177(a)(2)(i) says (emphasis mine):


  In the case of operations over an area designated as a mountainous
  area in part 95 of this chapter, an altitude of 2,000 feet above the
  highest obstacle within a horizontal distance of 4 nautical miles from
  the course to be flown; or [...]


If you then go to 14 CFR 95, you'll see that it defines mountainous areas by latitude and longitude. It's entirely useless for practical purposes, but at least it's precise :-)

As for the MOCA, I can't find anything to support the different definitions that you mentioned. 95.1(e) simply says:


  (e) The MOCA assures obstruction clearance on an ATS route, ATS route
  segment, or other direct route, and adequate reception of VOR
  navigation signals within 22 nautical miles of a VOR station used to
  define the route.


The AIM and PC/G support that; there's no other definition that I could find.