If you want to make that Burmese curry or find that weird cheese you're going to have to go to the specialty shops. While it's possible to list dozens of obscure neighborhood ethnic markets, chances are you as a visitor will not be cooking and you as a resident already know where the little places near you are, so for expediency's sake we'll stick with the major locations. Barry Lazar wrote a book called "Ethnic Guide to Montreal" a while back, and this is the definitive guide to exotic food in Montreal. However, good luck finding a copy, as it has been out of print for a while. Prepare to wait 4-6 weeks at Chapters and Amazon. Some of the info below is from the book.
3588 Goyer (737-2383)--opposite the Plaza Cote-des-Neiges
This place is a paradise for Asians. Practically every nationality is represented here--I'll bet you can find an instant curry from the isolated Hmong hill tribe somewhere on these shelves. There's a whole aisle for ramen and assorted add-water snacks and soups, as well as dozens of kinds of dried noodles--Japanese-style men and soba and plenty of Chinese and Vietnamese varieties. If there is an Asian sauce available in Montreal, it'll be here. There's also a frozen section and a meat/fish/poultry counter, as well as a large and varied vegetable selection. Here is where you'll find your lemon grass and galangal. There's also a large selection of Caribbean foods. The clientele is a pretty equal mix of Oriental, South East Asian and Caribbean, and it's usually packed.
It's actually a little difficult to find, being on a side street (Goyer) just off Cote-des-Neiges. Take the 165 or 535 up CDN to the Plaza. This place has other locations as well.