With Amex you have many airlines (but NOT UA nor AA) to which you can transfer miles. Those include Delta, Continental, ANA (so there's a Star Alliance option), and I think Air Canada (also a *A option.) Of course, you cannot combine the Amex miles transferred into ANA with United miles, but you can get a ticket ON United FROM ANA after you transfer INTO ANA. In fact, if trying to get a Business (C) or First (F) award on other Star Alliance airlines, ANA is much more likely to have it available than does United.

You also have a totally different way of using the Amex points, which is to use them as money when buying a flight or a flight+hotel package on americanexpress.com/travel. There, you're not redeeming an award ticket, you are instead buying a regular cash ticket, but part of your cash is Amex Membership Rewards points which can be paid at checkout at 1 cent/point value. Not a good deal, but a way to use them on airlines that don't partner with Amex for transferring points in.

With Starwood, you can of course redeem then by phone or on spg.com for Starwood hotel stays. You also can transfer them to many Frequent Flyer programs. Most of them transfer at 1:1. Two of them have a horrible transfer rate, at 2 SPG points needed for 1 mile (Continental and United, not coincidentally both having their own credit cards issued by Chase, which made the airlines make their SPG-Airline transfer unattractive so that the Amex SPG card wouldn't be a better deal than the Chase United or the Chase Continental cards.) Starwood also has a "nights + Flights" deal which doesn't actually book the flight but includes a 50,000 mile transfer into a frequent flyer program (or I guess only 25K when into UA or CO.) If you transfer 20,000 SPG points, they throw in 5000 free at time of transfer, so for example 80,000 SPG points can become 100,000 Delta or Northwest or American or US Airways miles (but only becomes 50,000 UA or CO miles.)

You're probably best off using the SPG points for your hotels and the UA miles for your flights. That is, if you actually still have the UA miles. If you're so unfamiliar with how to use them, is it possible you haven't been using your UA account for a while? UA expires ALL your miles after 18 months of inactivity. Earning or redeeming even 1 mile at least every 18 months keeps them all alive. It used to be 3 years but they changed that retroactively in 2007. I hope you still have 1MM UA miles but you might have zero.