How to know if my walnuts are fresh enough to be good to eat?
Your best methods are to use the tools nature gave you:

Visually inspect the nutmeats; you should not see signs of mold or discoloration
Smell the nuts; they should not have that rancid odor, nor (according to Eat by Date) smell like paint
Feel their weight; they should not feel light or dried out, nor slimy or wet (although the latter is very unlikely unless they have been stored in wet or very humid conditions)

None of these are absolute, but together they give you the best indication that you can probably get at home.
I found several anecdotal accounts that the float test, also described by MaxS (the nuts should float in water) will help separate bad nuts, but I could not find credible documentation.
See also:

University of Minnesota Extension article on harvesting and curing walnuts
Do nuts ever go bad?
Can cashews go bad? If so, how do you tell?