recently I download my facebook archives, as a result of this download I no longer have assets to my computer.
Once I log-in the computer go to the setup page. I get several lines saying error 16. I cannot go to the grub menu, I cannot reboot and when I try to use my livecd for Ubuntu 15.10 it states I don't have enough drive space. Is there any way I can delete unnecessary files when I cannot get pass the set-up page.

A couple of options would be in the grub menu to try and fix it there by accessing the hard drive and deleting files.

I'm more of a proponent of instead booting the system using a live media such as a DVD or thumbstick and then deleting files to free up space.

This is all presuming that you understand what files are best to be deleted, which are some of your data files. And actually instead of deleting them, you can move them off to another USB mounted disk, so as to remove them from your boot system, but not lose them entirely.

Error 16 sounds like legacy grub - that probably means an old system. That error states - "Inconsistent filesystem structure".
Probably needs to be fsck'd - could be done from the Ubuntu liveCD so long as you don't try to install.