"They like us."
Translation:Ils nous aiment bien.
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).