It would appear that angels do have languages since they are intelligent beings, self-aware, and communicate.  We know they can speak in human languages, as was the case in biblical times with Abraham (Genesis 22:11), Gideon (Judges 6:12), Joseph (Matthew 1:20), etc.  We also have a statement by Paul that says, “If I speak with the tongues of men and of angels, but do not have love, I have become a noisy gong or a clanging cymbal.” (1 Corinthians 13:1).  This could mean there are multiple tongues of men and various tongues of angels or tongues “plural” of both men and angels, where there is only one angelic language.  We don’t know for sure.  Nevertheless, it seems evident from Scripture that angels have languages.