Converting unit/mg or unit/ml into ng/ml, or vice-versa
There is no archaism in measuring enzyme amounts in units. Unit definition for SOD and a protocol can be found here (from Sigma): https://www.safcglobal.com/technical-documents/protocols/biology/enzymatic-assay-of-superoxide-dismutase.html :

"One unit will inhibit the rate of reduction of cytochrome c by 50% in a coupled system, using xanthine and xanthine oxidase ..."

I don't think, there is a good way to convert ng's to units, since one measures either mass or enzymatic activity, and the correlation between them is not always consistent. Units should be much more reliable in terms of comparisons with other studies, if you are not considering your enzyme as, e.g., a nutritious substance.