The LIMMA package has 3 algorithms for doing  "enrichment"-style analysis:     camera, roast, and romer.

A general, comparative overview of these 3 algorithms would be very helpful for the community (and me, too), 

At first glance, the 3 algorithms sound almost the same.  Understanding their differences requires careful reading of the papers and a strong  understanding of statistics.  Not everybody has the time dive into the details of the algorithms to understand the differences.  And even then, not everybody will understand the differences.  And even then, not everyone will apply the right test in the right situation.

Maybe a general overview:  what is the hypothesis tested by the algorithm?  What assumptions does it make?  At what level of differential gene expression is the test applied (after calling DE genes, before, etc) ?  What are the "typical" scenarios for each test?  Etc.

Well, the difference between roast() and camera() is stated concisely in first paragraph of the Details sections of the help pages for each of those functions, and the hypothesis tested by each of those functions is stated at the same time. What are you reading that makes them "sound almost the same"?

romer() is analogous to the Broad Institute's GSEA software, and no one has ever been able to state concisely what hypothesis that tests.