I really want to install VBox on Debian Wheezy but it seems it doesn't support new kernel. Here's what I got:

Is there a way to run it?

Do you have the packages mentioned in the warning installed?
virtualbox-ose-dkms
linux-headers-amd64

Regards

yep

You need to modprobe or insmod vboxdrv, which you've probably already done. VirtualBox has kernel modules it needs, which means they need to be recompiled for each new kernel, which you may not have done.

I didn't modprobe it. I'm kinda noob in these kernel and modules things. Can you explain it to me how do I do these things?

As root, type:

...at a command prompt. You'll also want to add it to your module autoload list, which I'm not sure how to do in Debian, but that shouldn't be had to find out. You could also load it every time you start VirtualBox, but that would be a hassle.

Now that's strange. It says the module is not found. But it should be loaded at startup according to virtual-ose config file. Any ideas? I'll keep diggin in google.

If the module is not found, it's probably not installed. This: http://wiki.debian.org/VirtualBox#Troubleshooting says that you may need to install the modules package, there are also instructions for making the modules load at boot. You'll also want to make sure your user is in the right group (vboxusers).

If they don't have a module package for your kernel version (which they should if you've been getting all your packages from apt) you'll have to start installing from source.

Once the module is there, you should be able to modprobe it... or just reboot if you set it to load at boot.

I have the packages installed. I don't have virtualbox-ose file, but I have virtualbox file and vboxdrv loading is set to 1.
So I think the issue is the kernel. When previously I was using Squeeze and had 3.x kernel from backports I couldn't install virtualbox as well. It's like they don't have support for this kernel or something. So I knew before installing that I will have problems with it.

I can assure you that Virtualbox works fine on 3.2.0-4-amd64.
It might be worth purging VirtualBox and re-installing whilst making sure you have the dkms and kernel source packages so a driver can be compiled.

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I purged it. I have kernel 3.2.0.3-amd64, however there are no headers for it in repos. There are only 3.2.0.4. I downloaded it. During installation of vbox it said "Building only for 3.2.0-3-amd64"
I think I should compile the newest kernel, but how do I do that? I always got that automatically via apt-get upgrade.

It might be the repos have the wrong packages -- I always just grab the source for my kernel and go.
Is Wheezy still testing?

I heard it is frozen. So it's like it's almost ready for stable.

So the problem was no headers for 3.2.0.3 in repos. I've upgraded the kernel to 3.2.0.4, installed headers and virtualbox was finally able to build module.

In testing and sid you should upgrade regularly.
As the 3.2.0.3 kernel was replaced by the 3.2.0.4, it and it's headers were removed from the repo (still available in snapshots if though).

I do update regularly, but somehow the kernel wasn't updated.