Am I right in thinking that these are only ever used reflexively, as in 'I wash myself' and 'Fred should push himself to work harder in lessons'.
Am looking at school reports (as you may have guessed) and have found a plethora of 'Myself and the teaching assistants are here to help' and suchlike.
I would substitute 'me', but, in the above example, 'me and the teaching assistants' sounds a bit... common wrong, along the lines of 'Me and Fred are ...', which I know should be 'Fred and I' but DYSWIM?