What does "rejected even" mean?

rejected is not with even as a word pair.  They follow each other because that is how the sentence works.  US Senate rejected.  what did they reject?  even a highly conditional membership.  even is a limiter, a way to say that the smallest thing was seen as unacceptable, never mind larger or more comprehensive things.  It is a way to define the limited extent of the thing that was rejected.

Even is not associated with rejected in any linguistic sense.  It applies to the "membership" phrase.

It means i got rejected 1 time, rejected odd but i got rejected TWO times? Rejected even.

"Rejected even" isn't an expression.  "Rejected" means "refused to accept."  

In this context, "even" means "to that extreme."

Senate rejected membership in the World Court.  Even with lots of conditions.

It means that they decided against putting the needs of the United States second to that of a world authority