You've got a product already. Congrats. That's a good start. I fear for you slightly in that you've done the thing that many people do - sink a whole load of investment into a project and do a big bang release and pray that it succeeds. Do you know what success looks like?
On approaching VCs - your hit rate from cold calling is likely to be painfully low. Instead take a leaf out of the inbound marketing book - make them come to you. Generate a buzz, get noticed by bloggers and other influentials. When you have generated some awareness just make it clear that funding might be considered.
Do you have a plan for how you are going to make money? Have you made any money yet? At the end of the day, most investments are going to be on the back of a plan that looks like it is going to generate cash. Ok you might look around and see other social network sites that didn't focus on generating money for quite a while, but then they managed to pull in hundreds of thousands of users, no scratch that, millions of users. Now with millions of users you don't have to have a very strong monetization plan to still look attractive to investors.
Offshore dev team. Clearly you've been working with them for a while and you have a good feel for whether they are delivering to expectations. If this is working for you, then stick with it. If the people coming up with the innovative new ideas can articulate them clearly enough and they get implemented without too much grief then great - keep on going. There isn't a magic formula for success that says that you must have a local dev team in order to succeed.
Delegating marketing. I hope you understand what you're doing here. For a startup, it's all about marketing and awareness. You might have a great product, but if people don't know about it then you're stuffed. It's marketing (including word of mouth) that is going to drive user signups. And marketing is hard. Outsourcing marketing might work but remember that it isn't their livihood or investment that is depending on this working. Often it is only the passion of the founders that gets a startup over the first few hurdles.
Marketing locally vs nationally vs globally. Most people start off locally because it seems easier. Often it is easier because the systems are not yet ready for multi-state multi-country functionality. Also for a social network I'm guessing you need a critical mass of connected users before they will start participating more fully and perhaps this is more likely to take off if you concentrate your efforts to geographical regions. But you know your product and what drives user growth.
The best strategy is investing $100k of your own money and then not needing any more money. You end up owning the whole business and not being fleeced by the VCs. But in reality if you don't have a revenue stream you're going to need more money. Don't discount Angel investors who might be easier to get the attention of. They might be able to mentor you as well.
Keeping full time jobs whilst building a startup... now that's a tricky one which is always going to depend on your personal circumstances and your attitude to risk. If you are single with no dependents and nothing to lose with a bit of money saved up to keep you going then maybe committing to the startup full time is viable. Sometimes you can only pull these things off if you do commit full time as startups take lots of effort. However, unless you've got a rich uncle money is going to be the issue and without a revenue stream it'll soon start getting hairy. What would be great is if you could get the site to a stage where you've got a decent amount of user-growth and awareness - essentially a functioning prototype that entices the investors enough to fund you so you can leave your other jobs and work on the startup full time. Unless you can see a clear path where you can work full time on the startup and afford to live I'd say you'll have to wait it out a bit longer.