They will have the ability to develop an oral language much like ours, but the details will depend a lot on the precise anatomy of the mouth, especially the lips.
Unless they cannot close their mouths completely due to their tusks (which is highly unlikely), I think they will have no trouble producing bilabial stops (/p/, /b/ and nasal /m/). Even if the lips cannot seal the mouth, if a reasonable length is closed, the "popping" effect of a bilabial stop can be achieved. It may be that these sounds will not be distinctive enough, though.
The same goes for labiodental fricatives /f/ and /v/, which don't need full closure of the lips. Indeed the tusks could conceivably function as a secondary fricative articulation.
They might run into trouble pronouncing rounded vowels (such as /o/, /u/ and the front rounded vowels of French and German) and the consonant /w/, if the lips are not flexible enough or the tusks are too close to each other.
As for new sounds, I'm picturing maybe a bilateral fricative or approximant made by letting air out the corners of the mouth, left and right of the tusks, while the lips are pinched in the middle. You can do this yourself if you pinch your lips right behind your nose using your index finger and thumb and forcefully blow some air.