You would benefit from taking voice lessons with a teacher, so that the teacher can give you feedback on what they are hearing, and teach you how to pronounce things better.
It also has to do with pitch and melody, because when you sing at the top of your range, you naturally need to modify the vowels to accommodate the pitches. This is hard to explain in writing, but a voice teacher can demonstrate it for you.
Also, it is helpful to make recordings of your singing and analyze them yourself. Any kind of inexpensive recorder will do for this purpose.
When you are learning a song or a rap with a lot of words in it, practice with a metronome and start at a substantially slower tempo. Make sure you can articulate every note and syllable cleary (again, making a recording of yourself helps). Then sing a difficult phrase again and again at a gradually increased tempo on the metronome until you reach the performance tempo. In other words, start out slow, and then practice until you can do the entire song start to finish at the proper tempo.
Feedback and constructive criticism from other people who have a good ear is always helpful.
Finally, I would point out that REM's "It's the end of the world as we know it (And I feel fine)" is a very difficult challenge for any singer!