A la carte is pretty bad value...
A few places that will deliver (though none are fantastic) are Boustan (lebanese pitas and whatnot) , Il focolaio really good pizza, alto for anything (their poutine and fries suck), sandhu for anything, pitarifique for pitas, wok cafe for chinese.
Ditto what SnackHappy said about your actual neighbourhood - Delta University is not the Old Port, but is close to Old Montreal and down the hill from downtown. Here's a thread that might help:
Restaurant delivery suggestions for Montreal (Old Montreal)?
Are you staying at the Delta on University? That's in what they call the International District. It's close to downtown and Old Montreal, but a bit far from the Old Port. There's not much take out there. Most non-fancy places are open for lunch and often only weekdays. I worked around there a few years ago and decent delivery options were few and far between on weekdays and non-existent on weekends. I don't know if things have changed much.
You could always use À La Carte Express although it's not very good value, or ask your concierge for some take-out menus.