I have been fishing a lake toward northern Indiana, and the last two times we went (yesterday and the week before) there have been fish hitting the surface about 10-20 feet away from the edges of lily pads.  I don't know if they are feeding, but they might be mating b/c it seems like you will see the backs of two of them bumping into each other briefly.  

 

I can't get a good look at what they are, and I can get them to bite at lures but not take a lure, so I think they may be smallish.  Any idea what these might be?  The lake has been there forever and is connected to several other lakes so there could probably be any fish local to northern Indiana in that place. 

Carp or shad. Could be feeding bluegill also

Carp would be my best guess.

^{If it was my lake my guess would be small bluegills fighting over water bugs.   The surface of my lake is alive with skimming bugs this time of year, in the calm at sunset they have a feast.  Try a fly rod and match the hatch...  could be fun...}

Sounds like one of my favorites, carp

I'm going to guess shad that are spawning. When shad spawn they'll splash around on the surface/shore chasing each other around and will chase and bump into your bait as well which could account for those "bites" you're feeling but not hooking up with. I would agree with carp minus the fact that you say they're striking at your bait, which all but eliminates carp as a possibility.