I would try to keep the car level when checking/filling the diff. As Andy suggests, get both ends on axle stands.
To check the current level you can stick your pinky finger in the fill hole and see if you are touching gear lube. (If your finger is too big, maybe your wife will get under the car and do this for you....ha ha ha.....)
Alternately, pump lube in through the fill hole until it starts to run out, and its 'full'.
Check the little pressure relief valve on top of the diff at the back RH side to make sure its clean and the little cotter pin in it isn't stuck. If you overfill a bit, it will tend to blow out this hole.