..are being cropped to about a third of their normal height on the main page and about two thirds of their height on the post page.
That is the correct behavior.
With this theme, each image uploaded will be cropped to different sizes based on this function in the theme.
function oxygen_image_sizes() {
add_image_size( 'archive-thumbnail', 470, 140, true );
add_image_size( 'single-thumbnail', 470, 260, true );
add_image_size( 'featured-thumbnail', 750, 380, true );
add_image_size( 'slider-nav-thumbnail', 110, 70, true );
}The 470x140 is what's shown at the front or archive page, the 470x260 is used in a single page. The other 2 sizes are for the slider.
Will I need to run "Regenerate Thumbnails" each time?
No, you can deactivate it AND delete it now. Only use it when changing theme or when there are changes in image size.