"They like us."
Translation:Ils nous aiment bien.
I'm pretty sure you can't use "eux" on its own like this. It can be used as an "emphatic" pronoun to stress the person(s) referred to. E.g. "Vous nous n'aimez pas, mais eux, elles nous aiment."
all right , but it's more correct to say " Vous ne nous aimez pas, eux nous aiment"
I found an example similar to this, so it may not be wrong:
Eux le savient; lui pas. (They knew about it; he didn't.)
"Advanced French Grammar" (L'Huillier, 1999, pp 510, 511)
So I think the effect of Eux nous aiment bien is something like "Well they like us" with a strong stress on "they." The contrast would be with the previous sentence (which, of course, we can't see).