"Read Only" Toshiba external drive

Was the drive formated with Apple's Disk Utility or did you use the Toshiba software? It's not uncommon for users to not format for Mac after purchasing an external drive. If it's still formatted as MS-DOS, I would recommend moving all the data off and formatting correctly for the Mac. Select OS X Extended (Journaled) when formatting. Disk Utility (El Capitan): Erase a volume

You can do a Get Info on the drive to change permissions, but you might have to reformat the drive using Disk Utility.

In the Get Info window, under Sharing & Permissions (toggle open to view settings), do you see a check box to ignore permissions. If not, is system set to Read & Write? You can click on the lock to change settings. After changing to Read & Write, select Apply to enclosed items. If Time Machine backups are on the drive this could take F O R E V E R.

I've seen similar issues myself with El Capitan. I've seen the Read & Write issue clear on it's own after an update to El Capitan.

Which third party software are you using?

Once you figure that out go to the web site for it and see it they have updated it yet.

One of the many reason I alway recommend that NTFS not be used on Macs. It causes for more problems then it is worth.

How is the disk drive formatted?

If it is formatted as NTFS then it is very likely that your third party software you installed to write NTFS needs to be updated for El Capitan.