You lucky thing - a walnut tree is a beautiful thing We had several when I was a child. Some varieties are self fertile, others need pollination from another walnut - even the self fertile ones fruit better if there's another walnut in the vicinity - we had such a rotten spring, although they are wind pollinated, I'm sure that if the pollen is continually wet from rain it will not pollinate as well as in a dryer season.
I think I'm right in saying that they fruit on old wood formed in earlier seasons, so it may be that following pruning it's lost some of the fruiting wood and may take a few years to re-establish regular fruiting. Also late frosts may damage the flowering buds.
Walnuts do need a bit of feeding - on the farm ours used to be mulched with farmyard manure - yours would probably do with a spring dressing of a balanced fertiliser (one with nitrogen and potash in it). If you choose to mulch with manure don't pile it around the trunk as this can damage the bark and rot will set in. It would be best if grass doesn't grow right up to the trunk; a small circle of clear soil around the trunk helps the tree to access moisture and nutrients better than if it is covered with grass.
And another thing, if you're in a rural area watch out for crows - they will take walnuts and leave the shells hanging on the trees- as children we were encouraged to play noisily near the orchard to discourage the crows - it seems it's an international problem -more information here http://farmerfredrant.blogspot.co.uk/2010/10/crow-in-walnut-tree.html and if you have squirrels around, they'll steal them too!
And when I was a child there was an old saying, "A woman, a dog and a walnut tree, the more you beat 'em, the better they be" ! As I can guarantee that at least two of those statements are totally incorrect, I have no faith in the veracity of the third but there's a theory here http://www.telegraph.co.uk/gardening/3314692/Beat-them-as-hard-as-you-can.html.