How should I state my affiliation and funding if I am not funded and have no academic affiliation? I started a project during my math/physics PhD but am now continuing with it from outside of academia, using my own time and funds to purchase resources. What are the conventions for stating my affiliation and funding when writing up this work?

In particular, do I need to/should I name my current (non-research) employer as one of my sources of funding? They have had absolutely nothing to do with this project, other than hiring me to do a different job; they have not endorsed it and should not take any responsibility for it. On the other hand, it is a general principle that funding sources should be disclosed.
For this project, your "affiliation" is independent researcher. Your "funding" is just self funded. Both of those are well known and perfectly acceptable. 

But be sure that your employer has no claim on your independent work. Some will have a claim, or will claim that they do. For some employers, permission is necessary.