Two things.
1.
The second INDEX function within your =IF
INDEX(East!A:A,MATCH(SMALL($W:$W,ROW(A1)),$W:$W,0) ))
This seems to be missing a ' ( ' or have an extra ' ) ' I think it
should end ' $W,0)) ' no?

2.
Could I continue this worksheet merge with additional sheets by adding
more INDEX function lines to the overall IF function? If so, what would
be the additional format?
Example: Add sheet "North" and "South".

<clipped
INDEX(West!A:A,SMALL($X:$X,ROW(A1)-COUNT($W:$W)))),
INDEX(East!A:A,MATCH(SMALL($W:$W,ROW(A1)),$W:$W,0) )
INDEX(North!A:A,MATCH(SMALL($W:$W,ROW(A1)),$W:$W,0 ))
INDEX(South!A:A,MATCH(SMALL($W:$W,ROW(A1)),$W:$W,0 ))
<continues