I think that the situation is even worse than you think. Apparently you
can't tax your car anyway because there's no valid insurance on it.
Quote: "If your vehicle is registered in Northern Ireland, you must also have insurance in place when your vehicle tax is due to renew".
Source:
https://www.gov.uk/vehicle-tax-direct-debit/renewing
If your car is currently on the road, I think that you might need to first get it moved off the road (by contacting a friend or perhaps, possibly, by contacting a garage who can tow it to their yard or somewhere else suitable).
Once it's off the road, you can then go for the SORN option. If the V5C is still at your home address, you'll have to tell a friend how to get into your house (and also where the V5C is), so that he can contact you with the relevant information so that you can use the online option:
https://www.gov.uk/make-a-sorn
If you've not got a friend who can help out, you'll have to print out these forms (or find someone who can print them for you, if you've not got a printer):
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/807217/v890-make-a-statutory-off-road-notification.pdf
and
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/849283/v62-application-for-a-registration-certificate.pdf
Once completed, you'll need to POST them both to DVLA (using the quickest service you can find for the job) together with payment of £25 in a valid form (which, as far as I can see, would need to be as a cheque drawn on a UK bank if you've actually got such a cheque book with you).
Alternatively, try PHONING DVLA on +44 844 306 9203, either to try to pay the £25 fee (as above) over the phone by card or to seek a different solution to your problem.
Things are, of course, complicated for you as a (normal) Northern Ireland resident, in that's it the DVLA in Swansea who deal with SORN matters but the DVA in Coleraine who deal with vehicle taxation. Should you want to contact the DVA (who will however almost certainly tell you that they can't help you tax your car until you've also insured it) try +44 28 9049 5914.
I'm not sure that contacting the local plod would be such a good idea. They might well just think "Thank you very much mate. It's not often that a car's owner actually tells us where we can now get it towed away from"!
Good luck anyway, Pumpjack!