The StdErr Prob is not the same as the p-value. p-values are generally labeled as Prob > Chisq or Prob > t. How to find the p-value for your analysis will depend on the platform you are using. You can find information in the JMP documentation, in this case most likely the Basic Analysis book, which can be found by selecting Help -> Books -> Basic Analysis. You can also find the documentation on the JMP website: https://www.jmp.com/en_us/support/online-help.html.
Cramer's V statistic is not given automatically in JMP. However, JMP does provide the necessary statistics in the Contingency platform to compute it by hand.
For 2x2 tables, V = (n11*n22 - n12*n21)/sqrt(n1.*n2.*n.1*n.2) , where n.i are the column totals and ni. are the row totals.
For other size tables, V = sqrt [(Qp/n)/min(R-1,C-1)] (where Qp=Pearson Chi-square statistic, R is the number of rows, and C is the number of columns).