You need to have it out (NB note carefully in mm how far the lock nut is from the axle end). The freewheel can stay on (suspect it will be very keen to do so!)
Roll the axle on a flat flat surface: I'll bet it's not bent.
Clean all, maybe a set of replacement (ball) bearings (from LBS) and then reassemble (with drive side locknut within a mm of where it was); grease everywhere; and adjust so it spins and there's (just) no wobble (will need cone spanners obv). Secured with nuts means the complications of allowing for compression with a QR is not an issue.