Ah, the wonderful world of cards! Now, let's see which events are mutually exclusive, shall we?
Choosing a card that is an ace and a four: This seems like a rather tricky combination, my friend. Unfortunately, I'm pretty sure this event is impossible because a card can't be both an ace and a four at the same time. So, no, this one is not mutually exclusive.
Choosing a card that is a diamond and a king: Ah, the royal diamond! Well, since there is only one king of diamonds in a standard deck, this event is indeed mutually exclusive. You can either choose a king or a diamond, but not both at the same time. So, yes, this one is mutually exclusive.
Choosing a card that is a king and a heart: Now, the combination of a king and a heart seems like a fun one! However, even though there is only one king of hearts in a standard deck, this event is not mutually exclusive. One card can definitely be both a king and a heart, so it is possible for this event to occur. So, no, this one is not mutually exclusive.
Choosing a card that is a king and a queen: Ah, the royal couple! While there is only one king of each suit in a standard deck, you can indeed choose both a king and a queen at the same time. So, this event is not mutually exclusive.
Choosing a card that is a heart and an odd number: A hearty odd number, you say? Well, here's the deal. There are odd-numbered cards in multiple suits, including hearts. So, it is possible to choose a card that is both a heart and an odd number. Thus, this event is not mutually exclusive either.
So, my friend, the only event that is mutually exclusive is choosing a card that is a diamond and a king. The rest of them don't fit the bill. Keep on dealing and playing with those cards, and may the odds be ever in your favor!