I'll see how many of these I can fill in:
Alabama (skipping the all-too-obvious Lynyrd Skynyrd song)-"My Home's in Alabama"-Alabama
Arkansas-"Arkansas"-Glenn Campbell
Delaware-if we're going by lyrics: "Level Head"-Bruce Carroll (contemporary Christian singer) "a one-night stand up in Delaware"
Iowa-"Iowa Stubborn"-from the musical "The Music Man"
Kansas-"Lonely Boy in Kansas"-Wendell Burton (another contemporary Christian guy)
Nevada-"Viva Las Vegas"-Elvis (I'm surprised no one else came up with this one already)
New Jersey-again going only by lyrics-"Convoy"-C.W. McCall ("well we laid a strip for the Jersey shore"--I'm assuming the Jersey shore is in NJ, right?)
Oregon-"Don't Take Me Alive"-Steely Dan ("well I crossed my old man up in Oregon, don't take me alive") I googled this to make absolutely sure this was the right lyric!
Pennsylvania (I'm surprised no one filled this in yet; there are lots of them either with PA or Philadelphia)-"Pennsylvania 6-5000"-Glenn Miller (ok, that's a phone number, but so what?)
South Carolina-"Charleston"-standard ("made in South Caroline") Sorry I don't know who recorded this; I've got the music in a Reader's Digest book and that's how I know the song.
Texas (there are a lot of songs with this one also)-"God Blessed Texas"-Little Texas
Vermont-"Moonlight in Vermont"-standard (I'm pretty sure I've heard at least one recorded version of this, but I don't know who recorded it)
Virginia-"Carry Me Back to Old Virginny"-folk song (this would be considered "politically incorrect" nowadays)
Washington-"Seattle"-Perry Como
Wyoming-"Git Along Little Dogies"-folk song ('you know that Wyoming will be your new home")
Sorry I can't give any artists on some of the really old songs. Dawn, I don't know the Osmonds' song "Utah", but since they are from there, it doesn't surprise me that they have a song w/that name. I was gonna say "Ford Econoline" by Nanci Griffith ("he was a Salt Lake City rounder"), but then I saw you had already filled Utah in.
BTW, I went back and changed my answer on Alabama--I did have "Stars Fell on Alabama" but didn't know who had recorded it (that's another one I know from one of those Reader's Digest music books). So I went with one where I knew who had recorded it. And as I said before, I didn't put "Sweet Home Alabama" because that is way too obvious (I'm surprised no one put "Sweet Home Chicago" for IL).