I hear the song "Ohio" by Neil Young as mostly being in the key of F. The intro/verse chord progression (Dm F C) is vi I V (6 1 5) in the F major scale. The chorus (Gm C) is ii V (2 5) in the F major scale. You can play F major scale patterns over both sections, although it's more correct to think of this as the D minor scale (D Aeolian mode) because the vi (6) chord Dm is functioning as the root.
Over the verse, you can also play Dm pentatonic because the vi (6) chord Dm is functioning as the root. This will probably work over the chorus too, or you can switch to Gm pentatonic. All the notes of both pentatonic scales are found within the whole F major (D minor) scale.
At the end of the chorus before the verse restarts are a few measures of D MAJOR. This is a key change (a type of modal interchange) and requires that you switch scales. Since there are no other chords in this section, you can use any type of D major scale, but I think D mixolydian (G major) sounds best. If you want to get a little crazy, then try G harmonic minor or G melodic minor. I don't hear Neil doing much more than a D triad with a 4th added.
Play Until Yer Fingers Bleed!
Mr. Desi Serna