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How's your visual memory? If it happens to be good, consider reframing from "learn what items are on the menu" to "learn what the (actual physical) menu looks like", which might help by giving extra structure (this dish is above that dish, these dishes are grouped together because they're similar, etc.) and by providing an extra exercise you can inflict on yourself (attempt to reproduce a copy of the menu).
Is there any consistent structure you can get a grip on? E.g., maybe there are three things X each of which comes with a "Super X" that includes a large soft drink and a complimentary shoulder massage from the chef, or something.
What does your memory actually need to be able to do for you? I mean, is this about retrieving specific items ("Excuse me, can you tell me what's in the Maximum Fun-Fun Ultra Super Happy Meal[1]?") or is it about fluently generating complete lists from a fixed list ("Excuse me, can you tell me all the soft drinks you offer?") or about doing nontrivial queries over the whole thing ("Excuse me, can you tell me what I can eat from your menu if I'm allergic to nuts, don't eat meat, and want to spend at least $6 and at most $25?")? These seem like quite different sorts of task and you might want your training to match what you're going to have to be able to do.
Have you eaten their food yourself? If there's some particular item you have difficulty remembering, would it help to buy one yourself and pay particular attention to what it's like?
Disclaimer: I have never been a waiter, never tried to memorize a menu, and have a very poor visual memory.
[1] You don't want to know about the other meal they offer.
[EDITED a couple of times to fix typos, once to add another, probably bad, suggestion, and once to provide a better TWC link.]