Nasal voices are due to clogged sinuses or sinuses that are small in size, are they not? You might try a nasal decongestant (Afrin or generic equivalent) plus a systemic decongestant to see if this makes a dif. Note this is not a good permanent solution -- rebound effect, side effects -- and may not help much to begin with. You can also try nasal douches with saline solution (made with roughly 1 tsp additive-free salt, read the label, Diamond Crystal Kosher salt is an example, to 1 cup water), and -- an otolaryngologist and sinus surgery if they find an infection. Personally I wouldn't want to risk cosmetic sinus surgery, to change the size of the maxillary sinuses, if they found no pathology.
You might also be able to make some improvement by changing how you "project" your voice -- taking just a few singing lessons, or lessons in a wind instrument -- where they show you how to breathe. Good teachers will show you this early on rather than concentrating, early on, only on getting the right rhythm and pitch. Breathing for yoga, and swimming, is similar.