Buy new grease fittings and replace the lot. You are wasting time trying squirt grease through old fittings.
The groaning noise from the steering sounds like you are: [1] low on steering fluid(ATF) [2] have air in the steering and it needs bleeding .
In both cases , open the reservoir with engine off . Remove the spring and metal plate and remove the filter in the bottom. Replace it with a new one.
On the steering box is a bleed nipple,get a length of plastic hose and zip tie to the nipple and open it,with the other end aimed into the reservoir and zip tied in place.
Refill the reservoir with clean fluid and let the car sit over night. In the morning , check and refill the reservoir then start the car and IDLE it. don't rev it!. Check the fluid as the car idles. it should have dropped ,fill it slowly while while watching the hose. Once it stops bubbling and clear fluid comes from it,get an assistant to very slowly turn the wheel from lock to lock . It should need a little more fluid and the fluid comming from the hose should be clear . Turn the steering a couple more times to ensure no air remains and top the fluid up to the mark on the side of the reservoir.
Turn the engine off and tighten the reservoir.
At any time the fluid is Pink and aerated and blowing from the reservoir,you have air in the steering box still which must be bled out.