Oxygen Theme Description http://theme.wordpress.com/themes/oxygen/ Live demo site http://oxygendemo.wordpress.com/

In Oxygen you can either have a Home page that displays your posts or a static front page ie. a Showcase template. http://en.support.wordpress.com/pages/front-page/#setting-up-a-static-front-page

Showcase page template
When you first activate Oxygen, you’ll see your posts in a traditional blog format but if you’d like to showcase your content in an online magazine-like fashion, then you can use the Showcase Page template. ...

Sticky post thumbnails are 750 pixels wide in the featured slider
Regular post thumbnails are 450 pixels wide
http://en.support.wordpress.com/posts/post-visibility/#sticky-posts
Oxygen
http://en.support.wordpress.com/featured-images/#setting-a-featured-image

If you don't see the page attributes module then make sure that you don't have it hidden in your screen options http://en.support.wordpress.com/screen-options/
Modules to unhide:
Post – Likes and Shares, Format*, Categories, Tags, Excerpt, Send Trackbacks, Discussion, Comments**, Slug, Author, Revisions, Writing Helper
Page – Likes and Shares, Page Attributes, Featured Image, Discussion, Comments**, Page Revisions, Slug, Author, Revisions, Writing Helper

Please be aware that you cannot crop the sticky post thumbnails.