Are overwing exits still useable if the flaps can’t be lowered? Essentially all narrowbody airliners (except for the very smallest propliners), and many widebodies as well,1 are equipped with one or more overwing exits for use in an emergency evacuation; these hatches, located at the window ends of rows of passenger seats, open (as the name suggests) onto the wing, from where, during a land evacuation,2 occupants escape off the trailing edge (almost never the leading edge, for some reason) in one of two ways:

On aircraft where the flaps reach within 6 feet of the ground when fully extended (the 737 is an example, as are most regional jets - DC-9, CRJ, etc.), the occupants simply slide down the extended flaps to the ground.
If the flaps don’t reach low enough on their own, as with widebodies, big narrowbodies, and the A320, one or more evacuation slides inflate from the exits over the trailing edge of the wing, providing a safe path down to the ground.

Either case presupposes that the aircraft’s flaps can be lowered completely; even if an aircraft has inflatable overwing slides, these are still designed to deploy over the lowered flaps (a slide designed to deploy over retracted flaps would trail on the ground with the flaps down, impeding egress from the bottom of the slide), while, with low-slung aircraft, the flaps are the slide.  However, many types of malfunctions can prevent an aircraft’s flaps from deploying fully, or at all:

A flap jam at a position other than fully-down will, obviously, prevent the flaps from deployed to the full-down position.
As flaps on essentially-all-but-the-smallest airliners are hydraulically-driven, a total hydraulic failure will render the flaps inoperable; on many-to-most airliners, even a loss of just one or two hydraulic systems will disable the flaps, as the flaps are less critical than the primary flight controls (the aircraft can still be safely landed with flaps retracted without much difficulty, while a safe landing with the primary flight controls inoperative is a crapshoot at best) and require a great deal of hydraulic force to deploy against the aerodynamic loads opposing their downward movement, making them a top candidate to be sacrificed if hydraulic-pressure-generating capability is limited (for instance, if all engines have flamed out and the hydraulics are running on RAT or battery power).

Do aircraft with overwing exits have special procedures for safely using the overwing exits in a land evacuation if the flaps can’t be lowered (or can only be lowered partway), or are the overwing exits simply unuseable on land if the flaps don’t deploy fully?

1: In some widebodies, the role of overwing exits is instead filled by full-size conventional exit doors a short distance forward and/or aft of the wing; these full-size exits allow for faster evacuation compared to the same number of overwing exits (which are limited in size by wing-root structural considerations), but create gaps in passenger seating, and, thus, are only used on aircraft large enough that the extra space required isn’t a problem.  Some widebodies, such as the 767, have both overwing exits and full-size near-wing exit doors.
2: In the event of a ditching, the water level typically comes all the way up to the wings, eliminating that particular problem (although creating several others).
The 737 doesn't have any special procedure for such a case. It would be the Captain's decision to use or not use the overwing exits. Factors such as the usability of other exits, the nature of the emergency, and the number of people on the aircraft would enter into the decision.