Talk of 'commitments' and 'obligations' in the above few posts somewhat misses the point. These are not easily-definable terms, and it is not always easy to distinguish between obligations of the EU and obligations of the member states.
For any 'court of law' (actually more likely an international arbitration panel) to make a ruling, it would need to identify where and how the UK has entered into a binding obligation to make a payment. The starting point is that Article 50 contains nothing about exit payments and clearly provides for the treaties to cease to apply on departure.
So where might a UK commitment have come from? The member states have agreed a multi-year funding framework (i.e. a contributions budget) which expires in 2020. I think there is a decent argument, rooted in basic fairness, that the UK should see out the remaining years of that funding framework. This is what lies behind T-May's suggestion that we continue paying during the beginning of our transition period.
There are also good arguments to say that the UK should pay for the ongoing costs (e.g. pensions) of British MEPs and Commissioners, who were only entitled to those pensions because the UK was a member of the EU and entitled to appoint those individuals.
It is far less clear that the UK should pay for things like expected CAP and regional development payments which have been budgeted beyond the multi-lateral funding framework. These are not UK commitments at all, but EU commitments. The EU's argument is that any future commitments made by the EU should be shared between the EU27 and the UK. This does not appear to have a basis in law - see the House of Lords committee opinion on this - and is really a consequence of the EU making pledges before calculating how they will be paid for in the next multi-year funding framework. It is conceivable that we might agree to contribute to these, but there would need to be a cost-benefit analysis done as to whether the payments were worth the benefits that we derive by way of trade deals.
I happen to think that it would not actually be too difficult to justify some of these payments, which is why I think the EU is starting to shoot itself in the foot by refusing to talk about the benefits which we may receive in exchange for payments. They gambled on a strategy of trying to force the UK to agree to large voluntary payments upfront. T-May's weakness is actually perversely damaging to the EU, because she simply cannot come back to the country and say that she has voluntarily spent billions with nothing in return.
The parties need to agree the easy wins (pensions, etc), declare 'sufficient progress', and just agree to come back to the divorce bill later. The EU could, I'm sure, recover quite a lot of their desired funds through transition period payments and/or EFTA-style contributions to programmes.