If a part doesn't seem to be taking any grease, wiggle it a bit. If this does not work you would need to replace the grease nipple. Continue pumping in grease until the dust cover of the suspension joints swells. Check the level of differential oil and manual transmission oil. Differential oil and transmission oil levels usually are checked by removing a plug from the side of the unit.
Most cars use hypoid type oil in the rear end.
For most rear-drive cars, the tube that is used in the rear end is also used in the manual transmission. Check your shop manual or owner's manual. Some of the new generation vehicles do not require to have the under chassis lubricated at all. Vehicles like the Maruti do not require under chassis lubrication. Only check for torn or damaged rubber bushings.