Summary statistic that can distinguish between migration from pop2 to pop1 vs. pop1 to pop2
Yes, migrants affect patterns of genetic diveristy

Immigrants yield to higher effective population size and therefore higher genetic diversity. They will also affect the site frequency spectrum and I would expect that if the migrants are numerous enough, they would yield to positive Tajima's D.

Therefore, unidirectional migration will definitely yield to differences in patterns of genetic variance among populations (that can be measured by any summary statistic of the site frequency spectrum). 

Existing methods for detecting directional selection

I have never had to do such inference so I am not able to do a good review of the existing technics. 

You should probably read Slatkin and Maddison 1998 and more importantly Beerli and Felsenstein 2001. Beerli and Felsenstein 2001 has been cited 1,341 times and you should probably quickly see whether some of these papers suggest more recent methods. John Novembre has some very interesting work on how to estimate migration rate between any two populations (e.g. Novembre and Stephens 2008). He might have done something of interest to your problem.

You can always use Approximate Bayesian Computation (ABC;see for example Jeffrey Jensen's work for example of inferences with ABC in population genetics) to figure out what pattern of migration is most likely. With a simple enough model, a good ABC algorithm is not that long (with good computing ressources). The question then is what statistic(s) to use for the rejection algorithm. Again for that, you should have a look at the existing literature to come up with a set of potentially useful statistics.