Pearson's chi-square was significant for 2 x 4 matrix. Calculated std. residuals for each cell to determine what cells contributed significantly to the model. Used +/-1.96 (corresponding to alpha = .05) for cut-off values for std. residuals. However, none of the std. residuals were greater than +/- 1.96 even though chi-square was significant. Any ideas on how to explain this outcome? Thanks so much...

Easy, all the Chisq test is doing is testing for deviation away from independance.

Imagine you re-created the contingency table using just the data from the marginals (the row/column sums), that would give you the expected counts in each table cell. Let us call this table "flat"

What the Chisq test is testing for is non-"flatness", which you have. That doesn't mean that any one cell is particularly non-flat, just that collectively they are not flat.