Is there anyway 'odd' and 'even' classes can be attached to node teasers so that they can be striped with different colored backgrounds? Is there anyway 'odd' and 'even' classes can be attached to node teasers so that they can be striped with different colored backgrounds?

In the same way that table rows can be striped.
Looking at the node.tpl.php doc page, there seems to be a way that you can print this in a node template. 

Put the following in the node.tpl.php file (if your theme has no node.tpl.php file, just copy from modules/node):

&lt;?php print $zebra; ?&gt;


You can use Views module to generate node lists in the exact same criteria that Drupal core front page has. 


Install Views module
There is a Views template called "front page" that you can edit.
Just save the View and make sure you have set the front page to this new views based page. 


By default, Views adds odd/even classes to the node list. You can toggle this feature in field settings. Choose "Row style" to "nodes" and under settings, toggle this feature.