You are right that resident landowners (or resident tenants and their children, parents, brothers and sisters permanently residing on the land) may hunt or trap on their farmlands without a license. BUT, Illinois landowners are still required to have a State Habitat Stamp to hunt or trap any species of wildlife protected by the Wildlife Code. Muskrat are protected by the Wildlife Code. The extended trapping season for muskrat is closed (as of February 15, 2103). However, since this is a nuisance issue (i.e., damaging the pond), you may be able to get a (free) animal removal permit from the IDNR district wildlife biologist (DWB). In your area, the DWB is Joe Rogus: (815) 476-2523.
Typically No. 110 Conibear® traps or No. 1, 1½, or 2 leghold traps are used to trap muskrats. All traps must be completely submerged so that non-target animals are not trapped. The traps should be placed in known muskrat runs to be most effective, and the trap should be positioned next to the den opening. All traps should be checked at least once a day. A nuisance wildlife control operator can be hired if you wish to have someone remove the muskrats for you.