Ubuntu 16.04 broken kernel packages won't let me install or remove anything with apt-get

Note: As ChaiT.Rex commented below, only steps 4 & 5 are required to fix the problem.

I leave steps 1,2&3 documented for anyone who may need to manually remove some packages. But try first this https://askubuntu.com/a/490677/26246 which looks easier.

  1. Remove them manually, be careful if you are retyping the below commands rm -rf is a dangerous command when it's run as root.

    sudo rm -rf /lib/modules/4.4.0-38-generic /lib/modules/4.4.0-42-generic
    sudo rm -rf /usr/share/doc/linux-image-extra-4.4.0-38-generic /usr/share/doc/linux-image-extra-4.4.0-42-generic
    sudo rm /var/lib/dpkg/info/linux-image-extra-4.4.0-38-generic* /var/lib/dpkg/info/linux-image-extra-4.4.0-42-generic*
    
  2. Change their status in dpkg status file.

    Make backup just in case

    sudo cp /var/lib/dpkg/status /var/lib/dpkg/status.backup0
    

    Find the related entries (command with expected output, line number will be different):

    ~$ grep -n -e "linux-image-extra-4.4.0-38-generic" -e "linux-image-extra-4.4.0-42-generic" /var/lib/dpkg/status
    18488:Package: linux-image-extra-4.4.0-42-generic
    77123:Package: linux-image-extra-4.4.0-38-generic
    

    Open status file for edit and change the package status:

    sudo nano +18488 /var/lib/dpkg/status
    

    from:

    Package: linux-image-extra-4.4.0-38-generic
    Status: install ok installed
    

    to:

    Package: linux-image-extra-4.4.0-38-generic
    Status: deinstall ok config-files
    

    Ctrl+o to save. Ctrl+x to exit.

    Make same changes to linux-image-extra-4.4.0-42-generic .

  3. Manually remove linux-image-4.4.0-38-generic & linux-image-4.4.0-42-generic too

    sudo rm -f *4.4.0-38-generic *4.4.0-42-generic
    sudo rm -rf /usr/share/doc/linux-image-4.4.0-38-generic /usr/share/doc/linux-image-4.4.0-42-generic
    

    Same as before edit their status to deinstall ok config-files

    $ grep -n -e "Package: linux-image-4.4.0-38-generic" -e "Package: linux-image-4.4.0-42-generic" /var/lib/dpkg/status
    61217:Package: linux-image-4.4.0-38-generic
    98051:Package: linux-image-4.4.0-42-generic
    
  4. Remove that troublesome virtualbox file

    sudo rm /etc/kernel/postinst.d/vboxadd
    
  5. Update dpkg status & grub menu

    sudo dpkg --audit
    sudo apt-get install -f
    sudo update-grub