I’ll bet you have an aluminum anode rod. That would give you the clear sludge. I’m guessing you probably also are not softening your water or there wouldn’t be much of the other kind of gunk.
I admit a conflict of interest, but still think you should put in my flush kit, which will enable you to flush more often and more easily.
As to anodes, if you are not softening, an aluminum/zinc anode will probably alleviate the odor, provided it is coming from the hot water. If it exists at one hot tap, but not another, it may be some other issue and putting in a different anode will probably be a waste of money and time.