Output:
WARNING: The vboxdrv kernel module is not loaded. Either there is no module
available for the current kernel (4.4.0-57-generic) or it failed to
load. Please recompile the kernel module and install it by

sudo /sbin/vboxconfig

You will not be able to start VMs until this problem is fixed.
5.1.10r112026

I think the trouble's not worth it. Doing all that stuff just to get 32-bit VM tasks is not nearly worth it, besides other VM projects don't have 32-bit tasks so until I get a VT-X system I am gonna run it without VM projects.

Thanks for your help as I did learn something out of this.

Just out of curiosity, would a windows installation be better to run BOINC?

Linux doesn't have stable ABI for kernel modules. That means compiled kernel modules work with only one specific kernel version. Most kernel modules are distributed with the kernel so you don't normally see this. VirtualBox developers however have decided that they distribute the kernel modules they need with VirtualBox. Since the host that will be running VirtualBox can run any arbitrary kernel version VirtualBox install package includes source for the kernel modules and the modules are compiled at install time.

Because the compiled modules are tied to the running kernel version it is necessary the recompile the modules every time kernel is updated. Now you might ask why this boring and repetitive task is not automated. Well, it is and the system is called DKMS. VirtualBox installer register its kernel modules with DKMS and when kernel is updated DKMS is automatically triggered to recompile all kernel modules registered with it. To work DKMS has one extra requirement beyond what VirtualBox requires for its modules - it needs to be installed.

Your package manager is apparently configured to install only the absolutely required package dependencies but not otherwise recommended packages. VirtualBox package doesn't require DKMS but recommends it. I'm not sure if installing DKMS triggers recompile or is it necessary to do the recompile that one last time manually. Either way, it's at most two commands and couple of minutes that's needed to get VirtualBox working again. Notice that even if you obtain VT-x or AMD-V capable CPU you'll still have to recompile VirtualBox kernel modules or automate the process.

It's quite possible that the missing DKMS contributed to your difficulties in getting 64-bit BOINC and VirtualBox to work together.

As for Linux vs Windows, I don't have much preference. Use whichever works for you.

He didn't use the package manager to install VirtualBox. When installing manually you have to manually reinstall VirtualBox in order to recompile the kernel module.

When using the package manager on Debian or Ubuntu this is all fully automated.

Oracle/VirtualBox provides repositories for the major distros. I have more or less always used the repository and I have never had to reinstall VirtualBox to get the kernel modules recompiled or do anything else for that matter. Looking at the filenames of the individual package downloads the files are the same as in repository. I haven't checked what the installer for not major distros does but it doesn't matter, we are not dealing with such distro here.