The phrase "walk drunkenly" refers to an unsteady gait usually indicative of being under the influence of alcohol. There are several synonyms for this phrase that capture the essence of the motion, namely stagger, stumble, sway, lurch, wobble, totter, reel, and weave. These words all imply a lack of balance and coordination and are often used in a figurative sense, as well as a literal one. While none of these synonyms sound particularly flattering, they are useful when trying to convey the notion of being inebriated or disoriented. So, if you ever need to describe someone who's had a few too many, you have several options at your disposal.