Would the remaining elvish strongholds help Eomer and his exile riders?

[Galadriel55]

Originally Posted by Victariongreyjoy

In the movie he gets banished from Rohan. Would the Woodland Realm, Rivendell or Lothlorien give him and the exiles shelter and protection if he travelled there?

I have not watched the movie in ages but here is a Books-based answer: until Eomer met Aragorn, Gimli, Legolas, and later some other Elves, he firmly believed, like most of the Men of his time, that Elves are in some ways even more dangerous than Orcs, and it is deadly to have dealings with them. Therefore, it would not even occur to him to seek refuge in an Elven abode.

If he somehow did plead his case in some Elven kingdom, I feel like they would turn a sympathetic ear - I feel that Elves do that whenever a mortal is brave enough to seek them out and speak their case. However, that also requires Eomer to speak to the Elves in the manner of, say, Aragorn in Lorien or Beren in Nargothrond - or even Frodo with Gildor. And he is more likely to take after Boromir in his attitude towards Elves, which would not bode well for him. *cue to notch*

So, in a books-based answer, pre-War Eomer would be highly unlikely to seek aid with Elves, but if he had done it - and properly - they would probably hear him out. As for assistance, well, that's a different question, and depends on what exactly that entails in that alternate reality.