I'd like to work with a freelancer who is based overseas however he does not have an offical company and only a personal bank account.
If he invoices me is it acceptable to pay in to his personal account?
If not, how else could I make payments, one thought was to use something like oDesk and setup a project which I award to the freelancer. I would then be paying oDesk (a legit company).
That's basically the freelancer's problem, not yours. If you're in the US - issue the form 1099 (get his W9, or more likely W8-ECI) and if required by the IRS - withhold and remit his taxes (check with your accountant). If you're (both) in countries with VAT - you may need to ask for VAT receipt from your contractor. How he deals with it on his side is not your problem.
Using US-based intermediate contractors saves you some hassle in this (you don't need to deal directly with the freelancer's tax reporting on 1099 etc), but it costs some money (which means you'll pay slightly more).
As you are in the UK its slightly different. Its the freelancers responsibility to declare their income so long as its clear that your relationship is a supplier and client. This is made clear by the contract between you.
As they are dealing with it essentially as a sole trader, you do need to ask them if they are registered for VAT (depending on where they are based). Most won't be as the level to start this is quite high. This does mean that you need to consider this in their fee. You can't claim back what you aren't charged assuming you are registered for VAT. In theory they should be 20% cheaper than a VAT registered company in the UK.
I don't see any issue in paying into a private account as such. My own concern would be whether I trust them to deliver if I had to pay any money up front and having a company creates at least a facade of professionalism. You need to think about liability should they cause you any issues. Do they have liability insurance? If they are overseas, would you have any method of recovering losses?
Yes (it is fine). Taxes and anything else are their problem. Make sure they send you an invoice before you pay. Then the record of the transaction between your banks is sufficient as a receipt.
(I was also going to say make sure you have a contract, but that falls under Business Commonsense, and is not strictly related to payment.)
People have been mentioning VAT; as far as I know this is not applicable, but it may depend on the two countries involved. I can only tell you with certainty about my experience of being a freelancer based in Japan:
The reason I think this is the same in all other countries can be shown with a recent example: I was looking at something on Amazon UK. The price was shown with VAT included, but free p&p. When I put it my cart and went to checkout to find out the overseas delivery price it ended up almost the same price! The price for me included p&p but now excluded VAT! Similarly U.S. companies only add sales tax on after they know which State you are in; and never add it on if you are outside the U.S.
*: For billing a local company, in Japan, the consumption tax is always implicitly there: even if I haven't shown it on the invoice. I.e. even if I didn't bill it explicitly, I am assumed to have collected it, and I will have to pay it out of my own profits. To complicate things further, I only have to pay collected consumption tax, if gross billings for the year are over 10 million yen. The situation in the U.K. is slightly different, as you pre-register for VAT (IIUC), and because of the different rates it sometimes makes sense to register voluntarily.