We need more information.
Firstly, which disk? Is the whole machine installed on a single hard drive, or is it 'just' the root partition ('/') that's full?
Seondly, what is showing 'read only filesystem'?
Thirdly, which files did you try to delete, and who were you logged in as?
In general, when logged in as root, you can delete anything that isn't running. This limits you to non-OS files, generally, but some of those can be pretty big. Which distro are you running?