I have heard great things about the VEF - Although it is not as popular as NSF, NDSEG or the like since it is only for specific group (Vietnamese), however it is still well-known. Fellowship is good since the school does not have to take care of you - in short, you come to work (research) for them free of charge so it boosts your chance in that sense. Also schools like to brag that their students are fellows of this and that. I know UIUC in particular has accepted many Vietnamese student sponsored by VEF.
Are you applying for M.S. or Ph.D. program ? Ph.D. is a research degree so emphasize on research - it is perfectly fine if your projects yield no good result, as long as you show research potential, you're fine. In your Statement of purpose, tell them briefly about the work, what you've done, discovered, learned ... any thing from there that you would like to pursue in the future.
LOR likewise is crucial, if it's from someone well-known in the field, can comment about your working capability, etc ...
Just curious, what school are you from ? You might think it's unknown but the admission committee probably do since they have looked at thousand of applications, hundred of schools over years.