Dont go to the pnw unless you are ready for a cold wet miserable time outside. Obviousley gear makes everything way more enjoyable but if you dont like waking up to ice on the top of your tent , snow sometimes. I was in eugene last december and it was 35 during the day and 15 at night. Barable at best when it rained but with libraries and late open coffee shops, finding places to dwell can be tricky since the homebums and junkies have made a lot of places bun proof.my favorite place was the library, oregon outreach for bums is great thou,All over the state actually has some sort of deop in or shelter, st. Vinney de paul gives out clothes vouchers, food boxes, propane for stoves and heaters, tents, its a great resource with a handful of others.
Get a good warm snow boarding jacket thats gortex or rain proof, a wool blanket and i mean 100% wool, ground pad with a good R rating. Dont wear cotton youll sweat and it retains water but will suck the warmth right out of you, synthetic poly blends and under armour long johns are ideal.
As for transut hitchhiking in oregon is a piece of cake. Your allowed to walk on the highways. Transit is great in most cities, hises or the max. Usually you can catch a city bus to almost every suburb sout or north east or west in portland. The coastal area is pretty dead during the winter and rainy seasons but it isnt immposible to enjoy. Anything north of florence is a puddle constantly thou. Not saying its any diffrent inland but its a good change from the big cities, the food banks and drop ins are sparse but there are some along the coast.
In medford i got a tent, tarp, backpack and 5 degree sleeping bag at the medford st. Vinneys with just my id and a mon to wensday drop in till 2 pm.
But thats as much of medford that i could say was good. South 10 miles in ashland they have nightly warming shelters there at diffrent churches, plus the locals are pretty okay if you dont run a muck too hard in thier city.
Trim work is easy to find and it is a normal gig on the table for a 100 bucks unless you have a ebt, a bum rumor i heard said it discounts you for a med card or works card. Or go guerilla grow and find a grower..
All in all id stay away from washington, its very cold and rainy. Seattle is amazing but not in the winter if your used to los angles or a climate with no dramatic season changes.
Good luck, and remeber smile your in oregon.