Udayana did not know about Quantum Mechanics.
I mean, neither did Sriharsa (or even Sankara). That'd be physically impossible. The things that they were concerned with are way different from what contemporary science is concerned with. And the Nyaya cosmoteleological argument, even if I don't particularly find it convincing, doesn't really seem to negate anything in QM? Cf. William Lane Craig's Kalam cosmological argument. It's related to the transcendental conditions of causality, which is a philosophical concept not prima facie linked with QM.
my position is that of an advaitist and a strong atheist (i.e., 'even the possibility of existence of God or soul does not exist'). That is not the usual advaitist position.
I see. That does sound more akin to traditional Buddhist (especially Madhyamika) positions on deity and the soul than not. Though I don't think the general critique would differ a whole lot, since the Nyaya critique of Vedanta builds upon their critique of Yogacara Buddhism.
Madhvacharya (my homage to him) was the strongest reaction to Sankara
Jayatirtha (the primary interpreter of Madhvacharya's work in the tradition) actually was heavily influenced by the Nyaya misidentification theory of perceptual illusion, where error in cognition didn't mean ordinary perception was indeterminate (as argued most famously in Advaita by Citsukha) and therefore in requirement of sublation into higher cognitive forms, but that it was the misapplication of some other natural kind than the one instantiated in the cognitive object (pramana) due to similarity between kinds and a defect in the cognizer. Where they differ is that Jayatirtha, pace the old Nyayaikas, claims that the object that the cognizier misidentified the real object as doesn't actually exist in memory, but is an actually non-existent entity, a real absence.
Nyaya-Vaisheshika' in their current form or 'Dvaita' do not constitute the understanding of all Hindus about God question (that will be a huge claim).
Right, I wouldn't claim otherwise. Navya-Nyaya is primarily found in the Sanskrit universities and the work of Indians (and some of their western colleagues) working in the analytic tradition of philosophy due to its complexity and generally rarefied method of philosophical analysis. A lot of it seems to have tenuous connection with soteriology, which is why its hardly popular among any lay people.
After all, Samkhya had its 'nireeshwaravad' position. I beg Sri Madhva's forgiveness
Right, yeah, that's my point. Samkhya was atheist insofar as they believed that their philosophy didn't need God, but at the same time they weren't Advaitins (if you see Vacaspati Misra's commentary on Samkhya, one understands the differences fairly clearly, since he's medieval Indian thought's best exegete as well as a Vedantin).