What are the most effective methods to start and finalize an offline transaction through online channels?

You might want to look at Freshbooks or Xero - they both are Invoice management softwares, you can record your transaction online, whilst you can conclude the transaction offline. Its one the best methods (I know of) to have records online for viewing, perform the financial transaction offline and if and when in the future, you want to integrate online payment solutions, both Freshbooks and Xero offer integration to 3rd party payment providers.