From my limited experience BA Avios points are difficult to redeem for international flights, esp. from where I live STL to PVG Shanghai. But I also heard BA miles is very efficient for the US domestic flights, the trick is also to find them. So here is how I did recently, for one way STL to LGA (New York). I used AA advantage account to search award flights first (note AA is the BA partner in the US), and I saw some openings. Then I go to BA site, search the same date, I got the award seats.
I have not done round trip or multi-stop in this case. This is something I will try next time.
(Update 04-20-2014) Today I booked the round trip ticket for STL to CLL (College Station, Texas), it costs 36,000 points plus $20 for 2 tickets. This is compared to 22,500 points + $7.50 for three STL to LGA (New York) tickets. It’s a bit more expensive for the round trip tickets, even considering breaking it into 2 legs, it’s 9,000 points per leg.
Also, I noticed the points guy has some good stuff (this one and this one) about redeeming BA Avois points.