It's normally recommended to grow carrots by seeding them directly in the ground as transplanted starts are more likely to fork (the strange shapes coming out rather than one nice straight carrot).  Of course, it's also tricky to get carrot seeds to germinate well.  Carrots need to be planted in loose soil that drains very well, and they don't like a lot of Nitrogen.  Thinning them can cause disturbance to the fine root hairs of the neighboring carrots which can lead to forking, too.  They also need very consistent watering.  Too much at once can lead to the splitting that you are seeing.  If they were in a particularly sunny spot, I'm sure the recent heat dome didn't do them any favors, either.

I've had many crops that look just like yours (if they came up at all).  If you want to try again, I'd suggest that you try planting from seeds (or seed tape or pelleted seed if you find that easier to keep the seeds well spaced) and covering them with light weight floating row cover that you can water right through.  There's no need to prop it up, just lay it loosely on the ground right over the freshly planted area, leaving enough slack so that the future leaves can push it up as they grow.  You can use pins to anchor the cloth or rocks, pieces of rebar laid over the edges, or boards also work well.  This will also protect them from insects that like to get into the roots.  Go easy on the fertilizer.  You can plant carrots for a fall crop in the Willamette Valley from now until late August.

Here's more information on growing carrots in your home garden.  And here's OSU's publication about growing vegetables at home.

Hi, Luanne,
Carrots come in a variety of colors like white, yellow, orange, reddish, and purple.  The shoulders (top of the root) of them can turn green if they are exposed to the sun just like potatoes do.  While you don't want to eat green potatoes because they contain solanine, green carrot shoulders are fine.  However, I've never seen a carrot where the entire root is green as yours seems to be.  If this carrot is the same variety as those in your earlier pictures and is therefor supposed to be orange, I think I would err on the side of caution and not eat it.  There's a possibility that this carrot didn't develop good root color because of the high heat we had recently, but I'm not sure enough about that to say it's fine to eat.

Root-knot nematodes can cause the symptoms you are seeing on your carrot roots.  Usually nematodes cause stunted plants in addition to malformed roots, and the leaves on your carrots (in the earlier photos) look ok to me, but it's a possibility.  If you want to avoid the possibility in future crops, plant carrots somewhere else in your garden.  Planting marigolds in the spot where these were can help suppress nematode populations.  You can interplant marigolds with carrots next time you grow them, too.

I'm in Washington County.  Growing what reliably grows well for you sounds like a good plan!