Since we moved to our new home, in a new state, I've had, twice, dreamed that I spoke German as well as others around me. The first dream, I don't remember any specifics, but the 2nd dream (just a couple days ago), I remember seeing a word in German. I found the word looking through a German dictionary online, "deichsel - nf. shaft, pole, rod, beam; long revolving bar used to transfer motion or torque to gears or other parts (Machinery)"
I can give other specifics if you'd like, but why do we dream in languages that we don't even speak?

Do you hear or have you heard other people speaking German in waking life?

Sometimes a foreign word is a better way of expressing an idea than the English word, so your mind prefers the foreign word.

Your dreaming mind could also be making a pun out of the sounds in the foreign word.

If you have never heard German spoken before, how do you know that the word you heard was German? Maybe you just heard a word that sounded like "deichsel" in your dream, but in your dream it nothing to do with German? Does the dictionary meaning sound like it would have made sense in the context of the dream?

You're in luck. Dreaming in a foreign language is among those dreams that is a common type around the world. Charles McPhee has collected these dreams and been able to assign meanings to those that are as common as the one you describe. Your dream falls under the heading of "communication dreams."

Hearing a foreign language suggests difficulty in real-life communications. This could be due to adjusting (as you might be due to your move) to a new school, workplace or new friends who speak "a different language."

There is a related metaphor in dreams where we dream we visit (or someone else visits) a foreign country. These also reflect a feeling of dealing with issues that are "foreign", strange, alien.

The word you saw--I believe you meant that visually--might contain additional meaning in its German form if, indeed, you had known it previously. If not, it may have meaning as an equivalent sound in English. Could it have been referring to a sound-alike, such as diesel? Just a thought.

In any case, I think your new move is the most likely explanation for hearing/seeing a "foreign" language in your dream.

Good luck and blessings in your new home!