E mixolydian- E F# G# A B C# D E
E Dorian- E F# G A B C# D E
E Minor pentatonic- E G A B D
E Major- E F# G# A B C# D# E
1st of all, notice how much they are alike. E major and E mixolydian only differ by 1 note. E mixolydian has a lowered 7th. Everything else is the same as E Major. 2nd, E dorian and E mixolydian only differ by 1 note. E dorian has a lowered 3rd. Everything else is the same as E mixolydian. all that has happened in my brief explanation is that you have gone from 4 sharps to 3 sharps to 2 sharps. Now let's compare the number of sharps to the related key signatures. ex. E major has 4 sharps (F,C,G,D). what key has 3 sharps? answer...A major (F,C,G). finally, D major has 2 sharps.
Therefore, you could technically play: E major over the E Major chord, E Dorian over the D Major chord, and E mixolydian over the A major chord (which is deceptive to notice because the bass note being played is C#, which is the 3rd of A major). The chorus "come bless the Lord, come bless the Lord..." etc. uses those 3 chords. (E major, D major, A major/C#).
The whole vamp of the song "oh that men would praise his name, praise his name til the end of the earth..." or something like that, is all E minor pretty much. Therefore, you can go for broke on E minor pentatonic licks.
There are more places to apply the options you mentioned but I think that if you see how these basic concepts apply, it will give you revelation on how to apply these scales and modes in more places. I hope this helps. If not, let me know and I would be happy to make a video clip.
May God Bless you and empower you with revelation.