The Ammodramus sparrows are extremely secretive and elusive during migration, acting like mice in often extensive grassland or weedy habitat. I've never found one by ear, but they do vocalize, and conceivably they could be discovered this way if a suspicious sounding call was heard.
The flight calls are distinctive, Le Conte's being a long, descending tinny call, like a lengthy Savannah. Henslow's is a longish trill, that sounds a bit like an American Robin to me. Grasshopper Sparrows have a rising call; the only other clearly rising sparrow calls in the east are Vesper and White-crowned (and the rare Clay-colored). Saltmarsh/Nelson's (Sharp-tailed) have high (higher than Song Sparrow), level, tinny calls.
Of course, in the field, it would be extremely difficult to pick out one of these birds by its call, amongst all the other calls by more common species. Having said that, we need all the help we can get, and challenging as it might be, I'd say it behooves us to learn their calls to perhaps increase the odds of finding these little guys.
Le Conte's Sparrow (Feb, PA)
Henslow's Sparrow (Oct, PA).
Grasshopper Sparrow (Oct, NJ).
Sharp-tailed Sparrow (Nov, NJ)