I've only worked for 2 lines (NCL and RCCL) and we're paid in USD twice a month - actual bills. US citizens have federal taxes taken out, and the only other deduction I've seen is for some Filipino crew.
Both lines had money orders on sale in the crew office. RCCL's crew office can wire money to banks in most countries provided a wire account has been set up by the crewmember.
Many crewmembers will hold on to their cash until the end of the contract (and take a big risk!) and many make a mad dash to the closest Western Union in the next available port.
I think to open an off-shore account, you need to have a SIGNIFICANT amount to deposit first - and your average crew probably doesn't have that
If you're based out of the States, some non-US citizens have opened a USD account at Bank of America. And getting a US based debit/credit card through BOA is handy for many.
If you have any bills or reoccurring debt - it's wise to make sure everything is online so to be able to pay them on time. Putting things in the post can be dodgy in some ports.