Glue and screw is one option.
Easy solution in case the original floor can be screwed into: put the thicker OSB ontop and screw it all together, shouldn't need glue and in case you have movement somewhere (test prior to adding the topping) just add a screw. Layering the OSB so the seams dosn't align helps.
Should you care about noise get laminate with cork backing and/or put footfall sound insulation below the laminate (adjusting the OSB thickness to the changed situation, the insulation is available as somewhat pressure resistant foam sheets in several thicknesses).
In case you like your ears and warm feet think about Cork (which is also available in click variants as the usual laminate) instead - little more expensive but for worst case you can sand it down should it (or the top coating should you go for a sealed kind) show signs of wear and reseal it (several times in case you pick the type with thick cork topping). Also more resitant to dropped stuff, localised high pressure (like from cabinets, table legs) might leave marks but it's quite easy to fix spot-damage in cork (compared to laminate).