Question: In the past I have used Khan Academy to great success to practice advanced math problems. It is useful because it gives simple questions in a multiple choice fashion then it quickly tells whether your were right or wrong, and it will walk you through the correct approach as needed.

Now I am in my first semester of a PhD in economics. Khan Academy has a series on economics, but it is no longer sufficient. The series is not accompanied with practice problems and it is done largely in algebra rather than calculus. Finally, there are a number of graduate topics it entirely misses such as:

1. Phase diagrams
2. Lagrangian multipliers to solve for optimal allocation
3. Compare/contrast of using different models for the same question (Austrian, Solow, Diamond, RCK, DSGE...)

If it helps, a primary course text is Romer's Advanced Macroeconomics, 4ed.

What are some online resources to practice such problems?

Answer: 
There are lots of good courses (economics, math etc.) on [MIT OpenCourseware](http://ocw.mit.edu/index.htm) or interestingly, there are also very very good lectures in YouTube.
But I think the web site for MIT opencourseware is a real treasure. (at least for me).
As far as I know, a lot of universities offer online courses that map closely to the topics you have mentioned. Coursera is one such online resource that amalgamates courses across universities. Perhaps you can check out Mathematics for Economics class if its available.