When I sing, speak, or rap I have a very sharp and peircing type voice (it's very foward) but when I put a bottle cap or a wine cork in the left side of my mouth my voice sound a lot more clear, vowels that I normally have problems with (short a, short, e, and ih) and would have to modify sound good already like I've already modified them, and my voice sound a lot more stable and firm. Why is this? What is the wine cork causing me to do that I'm not doing when I normally sing or speak? I know that's a bit of stretch because you'd have to actually hear me speak or sing to determine that but please share your thoughts and opinions on this. I'm familiar with resonance, and the concept on your voice not sounding to others how it sounds to you etc...
It would be impossible to say for certain. If you tested with recordings and think that your voice is more stable in a recording and not just in your head while singing then there might be a few reasons for this.
1) It is possible that your your larynx is lowered and your tongue is more relaxed when you have the cork in your mouth. I can't say that I know this to be an established vocal training trick. However, one of my voice teachers used to do an exercise with my where I would gently stroke the sides of my cheek in order to remember to relax the muscles in that area. The practice had a profound effect and it is possible that you are remembering to relax those muscles while the cork is in your mouth.
2) The difference between the sounds of vowels is actually a result of the overtones which are emphasized when we change the shape of our mouths. It is possible that the cork is suppressing errant overtones that make the vowel sounds more distinct and pleasing to your ear. You can see more here.