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The Nambuâ€"Jonaâ€"Lasinio model is considered with flavor-dependent coupling constants G i j ( ψ ÂŻ λ i ψ) ( ψ ÂŻ λ j ψ) + ( ψ ÂŻ i Îł 5 λ i ψ) ( ψ ÂŻ i Îł 5 λ j ψ) for i , j = 0 , 1 … N f 2 âˆ' 1 , and N f = 3. A self-consistent calculation of quark effective masses and coupling constants is performed, making the strange quark effective mass vary considerably. Quantum mechanical mixings between up, down and strange constituent quarks yield a strangeness content (s-content) of the light u and d quark constituent and of the pion. Different types of estimates for the strangeness contribution for the pion mass are provided. Mixing-type interactions, G i ≠j , induce light meson mixings, and estimates for the Ď€ 0 âˆ' η and η âˆ' η ′ mixings are provided. The η âˆ' Ď€ 0 mixing is argued to be an indication of the s-content of the pion. [ABSTRACT FROM AUTHOR]