Right-click or Control-click on a file you want to delete. When the pop-up context menu opens, press and hold the Shift key to see if the Trash option changes to another option which will delete the file immediately.
If you cannot open any apps, then your only option is to reboot the computer into Safe Mode which will delete some temp & cache files during boot among other things. Free up some more space while in Safe Mode making sure to empty the Trash or by deleting the files immediately.
If Safe Mode doesn't work, then boot into Internet Recovery Mode using Command + Option + R. You will need to use the Terminal app and the command line to try and delete unnecessary files or by trying to delete any APFS snapshots with the "tmutil" command. If you have another bootable macOS drive, then boot the computer with it to see if you can free up space on the drive.
If you are using APFS then you may not be able to resolve the issue except by erasing the drive and reinstalling macOS. This is due to how the APFS file system works and also because macOS allows the drive to fill up too far.