I had the same problem. Its because some other plugin also uses the Twitter OAuth API, and uses the same class to deal with it.
I could fix it by editing the simple-twitter-tweets.php
file, on line 408, replace this :
include 'twitteroauth/twitteroauth.php';
with
if ( ! class_exists('TwitterOAuth'))
include 'twitteroauth/twitteroauth.php';
This should be included in a future update of the plugin…
Dear plugin developer, could you merge this fix into the main branch ?