This is a two part answer. I sharpen straight razors generally on fine natural stones and then keep them sharp with a good linen and shell leather strop.
I've sharpened disposable blades before on a very fine hone followed by oxide on balsa, but the edge gets a little fatter when you do that - it needs to, too, as the platinum or chromium coating on the edge is gone when you hone and the underlying steel isn't as hard as we'd like (the old steel razors prior to stainless were a lot harder - like the gillette blue blades. There are blades marked with that now, but to my knowledge, they're all stainless blades and all softer, so we're not likely to understand why people could hone the older blades (they were harder).
The three pictures below are an astra blade with some damage (the edge is so thin on razorblades, they always dent or flex - we never wear them out).
The next is a picture of a blade hand re-honed on a fine stone and then graded chromium oxide powder.
And the last is one with a hair overlaid for scale (all taken under the same scope at 150x magnification. (I tried a buffer on the last one - the edge isn't able to survive the buffer wheel without getting too fat).
The second blade will shave fine with a little extra pressure (The rounding eliminates razorburn), but it's just not that sharp compared to a new blade and if you like that new blade feel (astras are about 12 cents each here), sharpening just won't satisfy.
A straight razor is full hardness through and through and will take a bright polish everywhere (little dots of stuff at the edge are just dirt or dust - everything looks big at 150x)