Woah that is soaked, my diff is different to yours but I would say that is deffo the breather and you problem.
It might have the wrong oil in the diff, you must have limited slip diff oil. Coma do one. You will probably need less than 2 litres for your tin plate diff.
The older cast iron diffs take 3 litres and the breather is on the top of the diff housing.
If I were you, I would sort the breather, then drain oil, remove upper filler plug first, ( they often sieze) then drain, replace drain plug, then add LSD oil via the filler until full.
Then see how it goes after a few good runs, then in around a thousand miles or so, drain diff again, then refil with LSD oil again. That will purge out any incorrect oil that may have been used.
When the oil comes out it might look grey and gooey, this is normal. It picks up the friction material, as it wears.
IF the breather was the problem, and oil was pressurised out of the prop shaft seal, chances are, it might have tried to squeeze past the axle seals and into your brake drums. So worth a look in here anyway.
Don't rush into doing the drums just yet, there is a technique for removing the drums easily, and setting up the play in the handbrake cable. There is a workshop down load and many posts on this.
Edit... forgot to add, that looks like your breather.
Uncle Rustic
