Freelance Teaching
Freelancing teaching is a much more viable option than it has been in the past. Business visas easily available in Hong Kong free you from the need to sign a contract with any one school, and loosening rules on where foreigners can live open up accommodation options that were previously unavailable.
However, this is still an option limited mostly to the larger cities - in many smaller places the local PSB are not yet used enough to foreigners to let them run around renting apartments and finding their own work - they want you under the protective wing of a school so they have someone to blame when you fall off your bike / get arrested for karaoke singing / have both your legs broken by an irate husband. However, it's the larger cities that have the most opportunities anyway.
Finding some kind of freelance work is rarely a problem - the entire country is calling out for English teachers, and many schools will be happy to employ a part-time teacher who has already sorted out visa and accommodation issues. Businesses meanwhile rarely need there own full-time teacher, but will quite happily take you on for a few hours a week when they need training in presentation skills or letter writing. You will obviously need a period to settle in and build up contacts - for this reason you might want to think about taking a six-month contract with a school while you do some research and get business-cards printed.
Freelance work can encompass a vast range of teaching - you could be singing and dancing in front of 40 giggling 5-year-olds at 11am, then jumping into a taxi to the International World Trade Building for a report-writing course with a small group of bright young graduates. You are unlikely to get a diary full of the kind of work you want right away, but if you make a good impression and keep filling your business card collection you should be ok.
Presentation and professionalism are much more important for freelancers - a school that has paid for your flight, organised your visa and got you settled into a new flat is unlikely to get rid of you for little things like turning up to class half-naked. A school that only met you two days ago and has had two other teachers drop off CVs that morning is likely to be a lot more discerning.
If you are going to try your luck at freelancing, I would recommend that you either have a) some freelance experience elsewhere, b) experience of living in china or c) deep pockets in case it all goes wrong.