Unable to restore/reinstall/erase from recovery
Probably the El Capitan installer tried to convert your traditional partition scheme to a CoreStorage volume and failed miserably.

Though a Logical Volume Group and a Physical Volume were built, it still misses a Logical Volume Family and at least one Logical Volume.

You may now either add a Logical Volume or revert to the traditional scheme:


Boot to Recovery Mode by holding cmdR
Open Terminal in the menubar Utilities->Terminal
enter diskutil cs list


To add a Logical Volume enter:

diskutil cs createVolume lvgUUID type name size 
with lvgUUID: UUID of the Logical Volume Group. It's the first listed.

Example:

diskutil cs createVolume 0E37A07F-7123-4AE4-9C3C-D51D0C05E47E jhfs+ "Macintosh HD" 100g

This will create a 100 GB journaled HFS+ volume with the name "Macintosh HD". To create one Logical Volume using all available space in the Logical Volume Group the following should work instead of 100g: 100% or 250g

Quit Terminal, open Disk Utility and verify the new volume "Macintosh HD".
Then use Time Machine to restore the backup.

If the creation of the LV fails some inner structures of the LVG probably are corrupted and you have to delete the LVG.

To delete the Logical Volume Group enter:

diskutil cs delete lvgUUID with lvgUUID: UUID of the Logical Volume Group. It's the first listed.

In your case:

diskutil cs delete 0E37A07F-7123-4AE4-9C3C-D51D0C05E47E

Deleting the Logical Volume Group will automatically create one new classical JHFS+ volume with the name "Untitled" occupying all available space on the disk.

Quit Terminal, open Disk Utility, verify the volume "Untitled" and rename it by erasing it. Then use Time Machine to restore the backup.