The language is called Lenape, just like the tribe. Unfortunately it is almost an extinct language with only a few elders, all 90+ in age, who speak it fluently.
You can hear some of the words by going to the Delaware (Lenape) tribal website's
language pages. They are in live audio format.
The sounds in Lenape are arranged differently from those in English. The Lenape's also lack the sounds of R, F, TH, V. They do, however, add the sound written as X (or ch in German) which sounds a bit like clearing the throat. There is also a voiceless L like in the Welsh language, and a voiceless W .
Many of the consonants in Lenape come in pairs, voiceless and voiced. They are as follows:
voiced B D G J Z ZH
voiceless P T K CH S SH