As Paul has explained, it's archaic/obsolete.
In the past, 'use' worked like any other modal verb, hence the form 'usen't'. It was just like 'wouldn't', 'couldn't', 'shouldn't, mustn't. For a while, 'use' was like 'need' and 'dare', with the alternative forms 'needn't' and 'daren't' and 'usen't', but the modal forms of 'use' have now disappeared.
'Usen't' doesn't sound wrong to me - simply very old-fashioned. It doesn't surprise me that many native speakers, especially younger ones, hadn't heard of it. If I were you I'd try to update your 1954 grammar book, though!