Keep writing dialogue. Not using dialogue is not an option. In rare cases, the characters might be fully established by their (mute) actions, but I repeat: This is rare. Although we usually rely on our sight much more heavily than on our other senses, it's mainly language through which we establish communication.
How to improve stiff, unnatural dialogue? My advise would be: Be honest. (This is similar to what @what suggested, just more character-driven. I don't care whether I can speak the way the character does, it simply must be true to the character.) To achieve this, I don't plot out the dialogue in advance, I simply have an idea of what the outcome of the conversation should be. Then I sit down, start to write, and just let the characters talk. The dialogue might be short or long, depending on what the character is going through in the scene - joy? sadness? anger? - and what his/her general communication strategies are. If you have a good understanding of your characters and a good idea of the plot - a plot that all characters are comfortable with, i.e. a plot that no character tries to break free from -, it will not be hard for your characters to come up with the topics and ideas that you have in mind for them.
Another thought: If you are interested in communication in general, maybe read some literature about that, sender-receiver theory and all. The best dialogue, on the other hand, that I could think of spontanesouly, would be in Oscar Wilde's "The Picture of Dorian Gray".