My logo on my wordpress site ( troide.co ) needs to overlap the menu bar like in this picture: http://imgur.com/zLIIFLh
I managed to do it before but made no backups and then updated the theme, over writing all of my code. The logo code at the moment is as follows:
First of all, if you are going to be making changes to the code, you really should be doing this in a child theme so that you don’t run into this problem of losing all your changes when the theme is updated - https://developer.wordpress.org/themes/advanced-topics/child-themes/
And make sure you make backups regularly.
Did you try to add a negative top margin to #logo in your CSS - margin: -10px 0 0; ? It’s not great to use negative margins too often, but in this case it should help.