Wordpress was auto updated to 3.7 and now some things have shifted

Two different questions here.

Anyway, the logo is not showing up now, it is only text and the image next to the phone number in the header is also missing. It was a linked image. How do I get those to show up now

Were you using one of the default WordPress TwentyX themes? If so, whenever WordPress updates, those themes may get downloaded again and blow away any modifications.  You should always make child themes to prevent this from happening. If not, please indicate which theme it was and check the version...it may be that one of your admins updated everything, including any themes and that would also remove header images.  To get it back, simply reconfigure it from Appearance | Header.

how do I disable auto updates from happening again?

Up until recently, WordPress doesn't auto-update without a third-party in the mix.  As of 3.7, WordPress will attempt to auto-update the core when a security patch is release (e.g. 3.7 to 3.7.1) but will NOT auto-update to the next complete version (3.7.x to 3.8).

So really, it depends on who/what is auto-updating the site.  If you are on some form of managed hosting, the host provider may be forcing the updates through for their own security peace of mind.  If a user is manually logging in and updating there isn't much you can do other than removing his/her permissions or asking them to not do that.

To manage the 3.7 auto-update going forward, please read this article by one of the core devs:

http://make.wordpress.org/core/2013/10/25/the-definitive-guide-to-disabling-auto-updates-in-wordpress-3-7/

The "relevant to your interests section" of the above is:

4. Disable only core updates.

The easiest way to manipulate core updates is with the WP_AUTO_UPDATE_CORE constant:
# Disables all core updates:
define( 'WP_AUTO_UPDATE_CORE', false );
 
# Enables all core updates, including minor and major:
define( 'WP_AUTO_UPDATE_CORE', true );
 
# Enables core updates for minor releases (default):
define( 'WP_AUTO_UPDATE_CORE', 'minor' );

There are also some filters you can use for even finer control, which override the constant if used: allow_dev_auto_core_updates (like updating from 3.7-RC to 3.7-RC2), allow_minor_auto_core_updates (updating from 3.7 to 3.7.1), allow_major_auto_core_updates (3.7 to 3.8). Return true through these filters to allow such updates, false to disallow.

Oops - didn't realise 3.7 did automatic updates!

I did see (after you pointed it out) that those particular links were coming from our old dev site. The weird thing is that the dev site was still up. So they should have still been pulled from there. I just now deleted the dev site and replaced the link url to the actual site url where the images are now. So what could it have been? All I know is that it was fine, then I received that email saying it had been updated to 3.7 and then those links and the background image were gone. Its now ok with the updated correct links but why would it have all disappeared if the dev site was still up?