My take on D&D languages:
Common: Whatever your language and accent is.
Draconic: German accent. It's a bit sibillant, and you know, nazis.
Dwarven: The typical scottish accent. If you're scottish it probably doesn't work
Elven: French. I think the stereotype is similar to french people and elves

Giant: hm... there's giant? Well, just speak as loud as you can (you know, 'cause they're big)
Supernal: An angelical choir sounds in the background, anytime you speak
Abyssal: Speak like goth singers. If your throat can handle it.
Deep Speech: Russian?
Goblin: For me they sound like the old ugly witches from children's movies.
Primordial: This one's interesting. I imagine it as several people speaking at once. Or Saruman at the top of his tower invoking that storm on LotR.