Luckily browsers don't have to know jack about these attributes, so long as they pass them on to AT.
However, this is clearly a form. You get to use something called fieldsets, for example the dimension options you have on the far right look indeed to be a group of form controls who are of the same type. They get a fieldset, and this helps you figure out how you'd group things. This is one of those examples where a table should be inside a form. The issue here is, as far as screen readers go, the primary type of element here will be FORM, not TABLE. Headers and axis attributes and table stuff will not necessarily translate to a screen reader, so I think the best way forward is to think of this as a form that happens to have inputs with both a label and a group name (legend). Figure out what a good FORM would be first, then use a table to reflect that structure.
Will this form ever be presented to the user again, without form controls but instead with the options they have chosen? If so, then at that time you will use the same table structure as you had in the form, but now it would make sense to use stuff like headers and axis attributes, etc since it would only be a table.
You did mention some items don't have all the options other items might have. I think you might need to work from, what are the greatest possible number of options an item could have and work backwards. Items with fewer options will either have empty cells there or simply fewer rows, cols or th's.
I still don't have a good enough idea of what the different options are to suggest a good form (for example, I see two things called type... obviously they must be two different sorts of "type"), but I think this will mean the labels will have to be more descriptive instead of relying on column headers only. Especially since, it doesn't look like an item's first "type" box (a textarea?) has anything to do with the Width dimension, does it? So a column isn't appropriate here at all anyway.
Keep thinking on this. Ask yourself, what are these things? This will help you come up with appropriate legends (and legends should be short, sweet and to the point).