Sheffer stroke the most important advance in logic? I think I once read, or heard, that Bertrand Russell once said that the discovery that all logical operators are expressible in terms of the Sheffer stroke was the most significant advance in logic since the publication of Principia Mathematica, and that had he and Whitehead known about it beforehand, they would have proceeded completely differently.

This is a really strange claim, so I imagine that I (or the person who told me) misunderstood, or misheard, or made it up completely.

If Russell really did say something like this, what exactly did he say, and where and when?
I have been reading the recent book The Evolution of Principia Mathematica, by Bernard Linsky. 

The quote in the post is in significant ways not quite right. It comes in the Introduction to the 1925 Edition of Principia, first page. Here is what was actually written, in full. 

"The most definite improvement resulting from work in mathematical logic is the substitution, in Part I, Section A, of the one indefinable "$p$ and $q$ are incompatible" (or, alternatively, "$p$ and $q$ are both false") for the two indefinables "not-$p$" and "$p$ or $q$." This is due to Dr. H.M. Sheffer. consequently, M. Jean Nicod showed that one primitive proposition could replace the five primitive propositions $\ast$1.2.3.4.5."

So Russell is saying that the greatest improvement in the second edition of Principia that is due to recent advances in mathematical logic, presumably by others, came from using the Sheffer stroke and an axiomatization based on the work of Nicod.  There are also significant changes in the description of type theory, but presumably that is not mentioned here because it is based on ideas of Russell. (By this time, Whitehead had bailed.)  

Russell is not saying that Sheffer's work is the most important development in mathematical logic of the previous fourteen years.
The idea of improvement that could have been brought to Principla Mathematica [PM] is quite misplaced! Replacing the primitive team {INCLUSIVE-OR, NEGATION} by Sheffer's (actually Peirce's or even... Chrysippus'!) NAND wouldn't have improved PM, at all.

Because, primo, PM is a piece of kindergaten charabia that should not have been written -- and published -- in the first place: it is nothing but an elementary exercise in formalisation (a rather long one, indeed). As a matter of fact, one can generate it with the help of appropriate software.

Even the idea of formalisation in PM is besides the point: in PM, like in Frege's Begriffsschrift (1879) or in his Grundesetze der Arithmetic (1893--1903) and in Peirce's pioneering 1885-paper, the formalisation concerns only a superficial aspect of logic, namely the (provable) formulas as expressing propositions and / or propositional schemes, not the proofs themselves: the concept of proof -- the central concept of logic, after all -- is left un-formalised in PM. [*]

Second, the handling of quantification (first- and second-order) in PM is seriously flawed and constitutes a considerable step backwards even with respect to Frege. (This is, by the way, one of Goedel's side remarks on Russell, not mine. Cf. Goedel's Russell's mathematical logic, in The Philosophy of Bertrand Russell, edited by Paul Arthur Schilpp, Northwestern University, Evanston and Chicago IL 1944, pp. 123--153.)

Third, the Russellian finding, meant to avoid paradoxes and the like -- namely the so-called ramified theory of types -- is a paradigmatic piece of muddy thinking: in PM, the so-called orders and the type hierarchy are introduced only in order to get rid of them, at a later stage (by the so-called Reducibility Axiom).

Fourth, the actual mathematics `formalised' (so to speak, i.e. in formularian terms) in PM is rather elementary. 

Finally, PM (actually Russell and Whitehead) has done more damage than good to the reasearch in (theoretical) logic, during the last hundred years or so. 



[*] The proof themselves have been first formalised by Nicolaas Gerrit de Bruijn and his students and collaborators at the Eindhoven Polytechnics (NL), about 40 years ago, within the Automath project (Automated Mathematics), since around 1967--1968. Cf., e.g., https://www.win.tue.nl/automath/ and my Abstract Automath, Mathematical Centre, Amsterdam 1982 [Mathematisch Centrum Tract 160] @ https://www.win.tue.nl/automath/archive/webversion/xaut021/xaut021.html.