Tracking clicks on each link separately
You can append a different query string to each link, which will allow you to track each one individually. Lets say your contact page is at mysite.com/contact. You can create several url's with a query string that lead to the same page. Ex:

mysite.com/contact?link=1

mysite.com/contact?link=2

mysite.com/contact?link=3

etc.

You can always append a query to a URL without creating any aliases or anything. Simply add ?key=value (obviously you can change 'key' and 'value' to anything you'd like). Google Analytics will track all of these separately.

The only downside is that Google Analytics won't batch all your contact page visits under 1 url anymore, but instead each different query will be listed separately.