DJ= (also deejay) Disc jockey.
A disc jockey is a person who selects and plays recorded music for an audience. Originally, disk referred to phonograph records, while disc referred to the Compact Disc, so today we spell it with "disc", but in the 80's, when CDs didn't exist yet, it was spelled with "disk". Today, the term includes all forms of music playback, no matter the source, so most DJs now use MP3, they use no disk or disc at all, but are still called DJ (how 'bout that?). A DJ maybe the person who plays the music on the radio (as in this song) or the person who plays the music at a disco. Today, some disco DJs got famous recording their own versions of famous songs, altering the original song or mixing two or more songs into one single piece.

CAUSE= (colloquial) because.

BORED TO DEATH= Very very bored.

IN JUST ONE BREATH= If you say something in just one breath, you say it very quickly and/or in one go, without pausing.

YOU GOTTA= (colloquial) you have got to, you must.

GET UP= Stand up, leave your seat.

GET ON= (colloquial) To continue. In this case he means "continue with your life, move on".

GET DOWN= (colloquial) to dance; to party.

YOU DRIVE ME CRAZY= I like you very very much or you give me lots and lots of troubles (here and in the following lines she refers to her boyfriend, not the DJ). Crazy, eh? The same expression may refer to two things completely different, so what meaning do you think she's using here? You have 5 seconds to answer: 5...4...3...2.. Yea, that was quick! What? Oh, sorry, you're wrong, it's meaning number 2, "you're giving me many problems", that's why she wants to die but, ta-da! The DJ appeared and saved her life... with a song! Yea, right.

YOU'VE GOT ME TURNING TO ANOTHER MAN= You make me look for the company of another man (because you don't pay any attention to me). That other man is the DJ, and his company is only through the radio waves. Do you think that may be technically considered cheating?

A BROKEN HEART= If you have a broken heart your lover hurt your feelings (probably because they don't love you)

HOPPED= Jumped. If you hop into a car, you get on the car quickly and energetically.

CHECK IT OUT= (colloquial) Listen to this, have a look at this, pay attention to this, see if you like it. But in many songs this phrase means nothing, it's just a cool phrase that they use sometimes to make it sound cool :)

LISTEN UP= Listen carefully.

DEEJAY= DJ (see above)

YOU BETTER= (colloquial) You had better (+ infinitive without to)= You should.
This phrase is used to give advice and it's followed by infinitive without to. I remember my teacher saying often "if a native speaker says 'you better' without 'had' then that's colloquial, if you say 'you better' without 'had' then it's wrong". Well, he was a great teacher but in my opinion totally wrong here, since most people never use 'had' here when speaking. Or maybe he was mostly thinking of writing.

FIX= To fix a problem is to solve a problem. To fix a thing is to repair it.

MIX= A musical composition which is the result of mixing two or more different songs into one.

YOUR MAN= Your boyfriend or husband.

MOVE OUT= Leave home, go to live somewhere else.
In this song it simply means "leave your boyfriend, break up with him", because they're not leaving together (otherwise she wouldn't phone him every night).

ON A DOUBLE= (slang) at once, right now. This phrase is probably incorrect because the right expression is ON THE DOUBLE. Originally this expression means "at a double speed, twice as fast".

DON'T LET IT TROUBLE YOUR BRAIN= Don't let it worry you.

CAUSE AWAY GOES TROUBLE= Because your problems disappear.

DOWN THE DRAIN= If something goes down the drain, it disappears for good or for bad. If your troubles go down the drain they disappear and that's great. If your work goes down the drain, everything you did was for nothing, you lost it all. The DRAIN is a hole in the street (covered by a grill) to collect water from the rain, so if something goes down the drain, you lose it forever. Well, yea, I know, sometimes in the movies you can see people trying to recover money, the car keys or a diamond ring that fell down the drain, and sometimes they get it back! But forget about it mate, it's only a film. If your diamond ring falls down the drain, you'll never see it back!

BASS= An instrument that produces tones in a low register, usually referring to a double-bass, which is similar to a guitar. This word is so stupid that you spell it "bass" but you don't pronounce it "bass", you pronounce it "base".