Found solution, that worked for me: cutting long story of tries and fails short, I uninstalled Java 8u144 64-bits and installed Java 8u144 32-bits and minecraft worked like a charm. It appears, that something in minecraft (some of its libraries) or some mods strongly rely on fact of been executed in 32-bit environment (at least for version 1.7.10, with which I struggled). I know, that Java code is XX-bit agnostic, but if it calls into precompiled platform-specific library, thats, where the culprit could be hiding. Well, I'm only guessing.