After obtaining my masters degree, I spent four years doing other things before returning to pursue my PhD. My advisor has a Dept. of Energy grant which has funded me, but the grant will not be able to fund me for my entire PhD program. I'll probably need another two years worth of funding to finish my degree. I may not be able to get a Teaching Assistantship, as they are limited at my institution. I've also noticed that I don't qualify for some fellowships (like NSF GRFP) because I am not a "traditional" student. What are some other options for students in the latter part of their PhD program (i.e. dissertation)? Particularly, for the field of computational science?
In general, you're in a very tough situation. Most of the "big name" fellowships are moving away from funding older students, on the relatively flimsy rationale that they're making a bigger impact by funding less experienced students from the start of their program.
There are a few programs that do support late-term graduate students; these are typically known as dissertation fellowships. Examples include the Ford Foundation Dissertation Fellowships, but these also have other restrictions associated with them (for instance, a commitment to a teaching career). Similarly, the Fisher Doctoral Fellowship primarily supports environmental and energy-related research, while the Merck Fellowship Program is for African-American students in biomedical-related fields.
So there are resources available, but they are certainly very limited in scope, and you'll need to make sure you meet all of the qualification criteria. The other problem for you is that these fellowships are typically only one year in duration, so if, as you say, you are two years away from finishing, you will need to find some means to finance one year of study, either through TA's or other sources of funding. In the meanwhile, you should talk with your advisor if there are other resources within the group to help you—at least partially.