Asian Grocery/Market in Portland area?
If you are more in the Saco/Biddeford area, a convenient stop is Trans at 129 Elm St. in Biddeford. Their selection is well curated, meaning small but meets my needs. Lots of fresh veggies, dry noodles; don't skip the freezer cases, and the closet full of rice. Interestingly, also great prices on bleu cheese and other diary.
SE Asian: Haknuman Meanchey, Forest Ave, or Mitpheap, Washington Ave.
Chinese: Hong Kong, Congress St. at St. John, right next to Dogfish. (Sometimes they truck in baked goods from Boston Chinatown -- I got egg pastry rolls there once that were still warm.)
Japanese, Korean & smattering of Indian: Sun, Congress St. in the Arts District.
The big Hannaford on Baxter Blvd often has Asian produce and also a pretty decent Asian grocery and frozen selection. (for a regular supermarket, that is)
Hope that helps.
My husband just reminded me about Vientiane, on Brighton Ave at the other end of St. John, which has good Thai takeout (I like their peanut sauce v. much), and is a dusty, faded-labels type Asian grocery as well. No produce to speak of but you can buy sauces and dried noodles and other non perishables. If you order food, beware the long wait at dinner.