'Vege out' means to be a vegetable. That means not using the head at all. When you say this, you are saying you don't want to do anything except relax. Another common way to use this is to say, "I'm vege-ing out in front of the TV." That means you are watching TV not thinking about anything.
'Wing it' means to play it by ear. Or in other words, do things without planning or do things as they come along.
Learn English speaking much FASTER by downloading the TalkEnglish Offline Package and submerge yourself with over 8,000 audio files and over 800 pages of lessons! Then you can study without Internet connection and also listen to audio files using your MP3 player at any time. Go to the English Download page and download today!