The animationOut issue is because of the way the menu CSS is done, specifically the left: -9999px; etc So the animation is occurring, its just occurring off screen. I believe the menus CSS was done that way (vs display: none) so things work w/o javascript enabled and just pure CSS. Superfish + hoverintent was/is primary used for a11y reasons.
So a quick fix to make animationOut work would be to add the following to your theme JS (the display none is taken care of already by superfish), is to add these lines after the menu lines.
$('#main_menu ul').css({left: '0'});
$('#button_profile ul').css({right: '0', left: 'auto'});
Thats only the main menu (note the button_profile is special so it expands to the left vs right to keep it on screen),
You can chain that call to other menus as well, just do it like:
$('#main_menu ul, ul.admin_menu ul, ul.poster ul').css({left: '0'});
Although you may find you need to adjust the numbers on a individual menu basis to prevent jumpiness, not sure really.
Also note you can control the animationOut speed separately form the In, just add speedOut: ### to the spuerfish call ... so for a really slow out effect.
$('#main_menu, ul.admin_menu, ul.sidebar_menu, ul.poster, ul.quickbuttons, #sort_by').superfish({delay : 300, speed: 275, speedOut: 1500, hoverClass: 'sfhover', animation: {opacity: 'show', height: 'show', width: 'show'}, animationOut: {opacity: 'hide', height: 'hide', width: 'hide'}});
$('#main_menu ul').css({left: '0'});
$('#button_profile ul').css({right: '0', left: 'auto'});