Thanks a lot for a good answer.
Go nice on me with technical terms, though. Ok? Even if I know the basic of how to knit a couple of cables together, I'm in no way experienced with electronics 
I read somewhere that the Arduino uno has a limit of controling around 300 endividual leds.. Becaue of the limited memory in the Arduino. Is that so? In that case, it seemd like I need two, since one side only will be 216 leds.
By the way. The strips I'll be using are these
As far as I know, they should be individually programmable leds. At least according to a youtube video that linked to them.
Good idea about the MSGEQ7 chip. That was something i didn't know about. When I googled it, I came up with this Sparkfun Spectrum Shield.
Seems like massive overkill for my project because they have 7 channels on each side. But I think I might make something out of it. Also, I would like to make the electronics as tidy as possible. What do you think?
Soldering IC's to PCB's is something I'm not very good at, so I think I'll try to go for ready made components as much as I can 
Also, when it comes to the IR, I think there are breakout boards for that. ( That's another term I'll never remember, breakout board
)
At the bottom of this post there is a schematic for a bias circuit that allows a line-level audio signal (like the output from your head-unit into your amps). You need to bias the AC audio signal because the Arduino can't read the negative half of the signal. In fact, it can be damaged by negative voltages and/or the signal can be "damaged" (distorted).
Does this mean that I can use the signal out from my amplifiers too? Seems like some of them has a kind of throught put of low level signals. And, of course, I DID know that the amplified audio signals would kill anything low voltage.. Just didn't think, lol..
I see that some recomend to put a resistor, 200 - 500 ohm on the data in cable for the LED strip.
Would I also need this if I was using signals from Line In?
I'm thinking that if the amp don't have a low level out, I could make a splitter of some kind on the Line in signal cables.
The only thing that worries me are if this could cause interference and "noise" in my speakers.
Yes. Each Arduino I/O pin is only good for 1 or 2 LEDs. And it depends on the number of "channels". A "normal" RGB LED strip is 3 channels. "Stereo" would be 6 channels.
For example, I "rewired" the strip lights in my van. My van came with four 14-lamp "rope lights" mounted in the ceiling. There's a "split" in the center. I wired it as eight "strings" with 7 lamps each. So, I made a 7-channel effect with all 8 segments operating the same. These are little incandescent lamps so just white light.
So, grnd is one channel, power is a second and the data is the third?
I think I have to use my power supply to run the 5v directly to the strips, as well as powering the Arduino. Just need to find one that can transform the 12.2 to 14.8v of the car.
Yes, I think I know what kind of light strips you mean. Sounds a lot like a Chevy Starcraft or maybe a Ford from around the same time.
I have a 92 Chevy Starcraft, but I have removed almost all of the original wood trim, replaced by some new stuff I made, and all of the lighting inside is gone. I mean the woodwork looks like it was made by the equivalent of a woodworking Stevie Wonder, and the lights was mainly broken, so..
Most of the electric in the car has been rebuilt and replaced. A never ending project, I fear 
Ok, I see how you made it
Not sure if that would look good here though. I'm thinking that maybe it would look better if the individual strip in each bundle of three would differ. What frequency they would run on might be of minor importance.
I'm not sure why it has to be wireless... Mine doesn't dim but I have a 3-way switch - Center is off, one position is all-on, and the 3rd position is the active lighting effect mode.
Well, there is several reasons for that. And the dimming is also crucial. But mainly, I need to be able to operate my lighting and my main monitor from anywhere inside the van.
I'll have swithces in my overhead console, of course, and also switches for the main monitor in the rear wall.
But I also have rebuilt the lighting in the centre of the roof, and there will be other features, like the door locks, maybe power windows and main parking lights that will also go on a remote. As well as pause/unpause the main stereo, and volume control.. And general dimming of all the lights inside the whole van. Like I said, never ending project 
I was just thinking.. What would happen if one put a dimmer on the main power to theese strips? I have dimmers on the strips I built into the inner roof lighting and they go on somewhere around 20% of full power. For now they are not remotely controlled, though. Just a 12v dimmer I got from a shop here.
Again, thanks for the links and the help 