I attacked Delphine and Esbern by mistake and now they attack me and kill me (I let them) and then I'll respawn and then they kill me. Then I'll go far far away and they'll follow me, kill me, and it keep's on going and going. I'll attack them but of course you can't kill someone that you need for a quest later on..
I need help what do I do..

They're essential. Attack them, they'll go into blackout mode. Then fast travel away. Stay out of that portion of the game for seven in-game days, then go back and they should be fine. If not, you'll have to use a strong enough Calm spell on them everytime you see them. Sorry.