There are predefined scenarios which can be implemented between ERP/CRM and OnDemand which work on several protocols.
But, if you are talking about a total different scenario, then I believe SOAP webservices are the only way and I know its possible on ERP side to create such service but I don't know how you do that. Try googling for that! 
Once you create that webservice, import it as External webservice into OnDemand and then send in requests through this service with all authorisations/arrangements set.