Synonyms for Slog (same or very similar meaning)
WordNet sense 1 (work doggedly or persistently):
plug away, keep one's nose to the grindstone, keep one's shoulder to the wheel, peg awayWordNet sense 2 (walk heavily and firmly, as when weary, or through mud):
pad, plod, tramp, trudge, footslogWordNet sense 3 (strike heavily, especially with the fist or a bat):
slug, swigFrom the ODE community, based on WordNetadd/edit