1.) Give a speech - I'm usually confident before I'm called on to go up, but when I get up there - in front of everyone - everything changes for some reason. When I see everyone's eyes fixed on me, my adrenaline and anxiety immediately sky rockets, and as a result, I usually black out. When I draw a blank, I grow hot in the face, I start talking faster, my eye contact becomes inconsistent, I start becoming fidgety, etc. My solution for overcoming this to prepare diligently without procrastinating. I need to slow down and give myself time to let the words come out of my mouth. Also, another thing that helps me, is if I'm able to walk every so often as I'm speaking. When I walk, it helps get rid of some of that nervous energy (for example, look at the way Chris Rock moves during his stand up, I like to move in a similar way).
2.) Being with a group of strangers - It's never easy being around a large concentration of people you don't know. It stresses you out because you don't know what to say or what to do without looking like a jackass. There is no solution for this, other than simply saying hello or adding something to the current discussion.
3.) Asking for a date - As a man, I desire companionship with the opposite sex. I admired women on so many levels, so much, that I scared myself into not approaching them. I would put them on pedastals because of my inferiority complex. However, as I've come to realize over the years, women are not these overly critical, savage beasts we men make them out to be. They're very forgiving and understanding, as well as very appreciative of us taking the lead. They're approachable, as long as we treat them like human beings and not like a prize that has to be won.
Most of my anxiety stems from these grandiose outcomes I set for myself. I get in the mindset of "I'm a failure if I don't either get a.) this woman sexually attracted to me, b.) her cell phone number, or c.) a future date. As you may well know, it never ends well when everything is result-oriented.
The anxiety lingers because it's something I've never done before. Therefore, I think once I can get over that initial hump, I'll get better and will want to continue doing it.
However, I have to learn to love and accept myself before I can even think about starting a relationship with another person. That will be the process.