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 Because Walnut trees are susceptible to blight it is  recommended major pruning be done during the dormant period. Dead wood can be removed at any time and minor cleanup to open the canopy can be done when there is a forecast for no rain for a period of at least a week after the pruning.

Older walnut trees need pruning every 2 to 3 years and if this tree has not be pruned for a long period of time the process of pruning should be a multiyear process. A good place to start is opening the inside of the tree and eliminating crossing branches. Larger trees may need the use of professional equipment to access the taller branches.A good rule of thumb is to not remove more than 20% of foliage in one year. 

Walnuts are a challenge to grow in the Northwest and most commercial growers have given up. The small nuts can be caused by a lack of boron in the soil or by the fact that the tree is a variety that produces flowers when conditions are not favorable to pollination.

The good news is since walnuts were once a large crop in the Northwest, there are plenty of articles on growing walnuts. See these sites for more information:

Growing tree fruits and nuts

https://catalog.extension.oregonstate.edu/ec819

Growing walnuts in the PNW

ir.library.oregonstate.edu/xmlui/bitstream/handle/1957/20433/em8907.pdf

Here is a link for more information on pruning.

http://ir.library.oregonstate.edu/xmlui/bitstream/handle/1957/22166/pnw400.pdf