Can I play unequipped on-the-table cards in combat?
One-shot items you are "carrying" can be used just like ones in your hand. From the rules*:


  All Items you have in play are considered “carried.” Items that are actually
  giving you a bonus are “equipped.” You should indicate Items that are not
  equipped by turning the cards sideways. 
  
  A Treasure card that says “Usable once only” is often called a “one-shot”
  Treasure. Most of these are used during combat to strengthen the munchkins
  or the monsters, and may be played from your hand or from the table.
  
  Cards in play may not be returned to your hand.


Thus the main things that change when you put a one-shot card in play are 


Pro: it doesn't count against your hand limit.
Con: other players can see you have it and can e.g. target it with steal-an-item effects.


Finally, I notice you are using the word "card" everywhere instead of "item", so I want to make sure you know the difference: an "Item" is any card with a gold cost (including "No Value"), and only Items may be carried. So if your hand is overfull with monsters and stuff, you'll have to give them to charity or find a different way to get rid of them.

*those are the base game rules, but to my knowledge none of the many other versions and expansions significantly change the rule in question.