When and where the concept of valid logic formula was defined?

It is always good to be reminded that what strike us now as absolutely routine definitions of core logical ideas often took a surprisingly long time to get pinned down.

I too would suggest Goldfarb's paper more generally as a good place to start if you want to know more about what happened in the development of logical ideas over the 1920s.

There is also a very useful and interesting fifteen page introduction to the reprints of Gödel's dissertation and his 1930 paper in Vol. 1 of his Collected Papers. This is by Dreben and van Heijenoort, and again explores the historical background.

For a third reference, there is a great deal of relevant material in 'The Development of Mathematical Logic from Russell to Tarski, 1900–1935', by Paolo Mancosu, Richard Zach, and Calixto Badesa, which is a chapter in Leila Haaparanta, ed., The Development of Modern Logic (OUP).

Goldfarb ('Logic in the Twenties: the Nature of the Quantifier'. Journal of Symbolic Logic 44 (1979), 351-68) suggests that the first precise account of first-order logical truth is to be found in Paul Bernays: Review of Behmann's Beiträge zur Algebra der Logik. Jahrbuch über die Fortschritte der Mathematik 48 (1922), 1119.