Hi Aaron,
The theme needs to create theme for use with the portfolio, blog, widgets and things like that. Unless you are literally not using images anywhere except inside posts (even then they are used to cut down on loading time in some instances) you'll need them intact.
Even still, you can try removing the functions that create them in functions.php:
//register additional image thumbnail sizes that should be generated when user uploads an image:
global $avia_config;
$avia_config['imgSize']['widget'] = array('width'=>36, 'height'=>36 ); // small preview pics eg sidebar news
$avia_config['imgSize']['post-format-image'] = array('width'=>630, 'height'=>999, 'crop'=>false); // big images for post format image and gallery posts
$avia_config['imgSize']['fullsize'] = array('width'=>930, 'height'=>930, 'crop'=>false); // big images for lightbox and portfolio single entries
$avia_config['imgSize']['featured'] = array('width'=>930, 'height'=>340); // images for fullsize pages and fullsize slider
$avia_config['imgSize']['portfolio'] = array('width'=>465, 'height'=>346); // images for portfolio entries (2,3,4 column)
$avia_config['imgSize']['logo'] = array('width'=>465, 'height'=>220); // images for dynamic logo/partner element
//dynamic columns
$avia_config['imgSize']['dynamic_1'] = array('width'=>446, 'height'=>151); // images for 2/4 (aka 1/2) dynamic portfolio columns when using 3 columns
$avia_config['imgSize']['dynamic_2'] = array('width'=>609, 'height'=>210); // images for 2/3 dynamic portfolio columns
$avia_config['imgSize']['dynamic_3'] = array('width'=>688, 'height'=>151); // images for 3/4 dynamic portfolio columns
Regards,
Devin