What’s actually going wrong? Is it layout, function, or what?
On the radio buttons, though they both need the same name to work (that’s HTML), you can’t give two elements the same ID (that’s CSS). And once you’ve given them unique IDs, you can use the "for" attribute on the label:
<input id="cfDeliveryMethod1" type="radio" name="deliveryMethod" value="Mail" eform="Preferred delivery method::0" />
<label for="cfDeliveryMethod1"> Printed catalog by mail **</label>
<br />
<input id="cfDeliveryMethod2" type="radio" name="deliveryMethod" value="Online" eform="Preferred delivery method::0" />
<label for="cfDeliveryMethod2"> Online link to catalog</label>
<br />
I pasted your checkbox code into the standard MODx 1.0.4 demo site’s contact form, and it looked OK (checked by default). Are you using the latest version of eForm? I seem to recall there were some problems with
retaining checkbox/radio button values on redisplaying the form in some earlier versions.

KP
Add: A litle further follow-up, after looking at
the wiki page and dredging more memory cells. Your radio button validation only needs to be on one of the set. So the following complains about your "Preferred delivery method" not being set if you don’t choose a button before submitting (NB required is set to 1 now):
<input id="cfDeliveryMethod1" type="radio" name="deliveryMethod" value="Mail" eform="Preferred delivery method::1"/>
<label for="cfDeliveryMethod1"> Printed catalog by mail **</label>
<br />
<input id="cfDeliveryMethod2" type="radio" name="deliveryMethod" value="Online" />
<label for="cfDeliveryMethod2"> Online link to catalog</label>