To change the styling you will need to change the CSS of/within your theme and reference the styles as described. Then you can have your Tweets displayed how you like.

For reference:
The Tweets are in a widget as with all widgets, and are a simple unordered list.

  • To make styling easier the <ul> has a class of Tweets – <ul class=”tweets”>
  • Each Tweet is a list item <li>
  • Each Time reference is an emphasised link (to your Twitter page) <em><a>

"Your Tweets your way" information above is referenced from here