Im just seeking for confirmation, is it OK to say that : "A strictly dominant strategy is a weakly dominant strategy too"? This would be usefull because for IEWDS we can eliminate strictly dominant strategies first.
Since you mention IEWDS, I presume by "dominant" you actually mean "dominated".
Any strictly dominated strategy would satisfy the condition defining weakly dominated strategies and hence be called such. And yes, strictly dominated strategies can (and should) be eliminated in the process of IEWDS.
The possible typo notwithstanding, any strictly dominant strategy would satisfy the condition defining weakly dominant strategies and hence be called such.