if you utilize your diaphragm and move your 'voice' from your head to your throat
Perhaps I've misunderstood your comments somehow, but this recommendation couldn't be further from proper singing technique! Proper placement of voice is in the palate, and using the sinus cavities for resonance. Trying to shift your vocalizations to your throat will result in a guttural sound, throat tension, fatigue, and ultimately vocal damage.
I'm a classically-trained baritone, with nearly 40 years experience. I've never heard of plugging one's nose as a vocal exercise.
Without being able to see and hear the OP, my guess is that proper jaw and mouth position would go far in eliminating the nasal sound. The correct position of the mouth should be in a vertically-positioned "O" (for the most part...of course this isn't always possible depending upon the vowels and consonants). A nasally sound can almost always be attributed to a horizontally-spread mouth.
Sometimes practicing with your hands on your cheeks to press the jaw open and correcting the mouth position will help until you can do it naturally. Use a mirror.
Also, remember that you can't really "hear" your own voice, and what might not sound right to you sounds right to everyone else. As singers, this is our "curse". We hear ourselves mostly through the bones in our head, not through our ears.
Hope this helps.
-Bruce