I was wondering...

-assuming i'm carrying an object (i have super strength), and i would like to make a close combat attack, do i have to use the object as part of the attack, or is it an option?
-so, assuming again that i'm carrying an object and my character has close combat expert on his dial (which i cannot use if i am using an object as part of an attack): can i choose to use close combat expert if i want to make a close combat attack or will i need to use the object, therefore not letting me use close combat expert?

any and all help is appreciated.

not optional, you have to attack with the object

(emphasis added)
You need to use the object whenever you make a close combat attack. You cannot choose not to use it.

The only exception being Mind Control (though I'm pretty sure Grodd is the only one with SS and MC on the same click).

LE Ultron 13, as well.

Well, that is covered as well in the rule excerpt I posted:
Mond Control does no damage, so it's covered by that rule.

BTW, E Lorelei, LE Jessica Drew, U Darkseid, V Martian Manhunter and Supernova Super Skrull all have Mind Control and Super Strength, aside from those previously mentioned.