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We aim to provide explicit formulas for values and derivative values along adirection of some generalized Hurwitz multizeta functions at nonpositiveintegers. We will express these values in terms of Bernoulli polynomials, andthe derivative values in terms of Bernoulli polynomials, of derivative valuesat nonpositive integers of the Hurwitz zeta function, and of derivative valuesat nonpositive integers of some generalized Barnes zeta functions. Then we willapply these formulas in order to compute the values and the derivative valuesat $s=0$ of the Witten zeta functions $\zeta_{\mathfrak{g}_2}$ and$\zeta_{\mathfrak{so}(5)}$. As an application, we will find an explicitasymptotic formula for the number of representations of dimension $n$ of theexceptional Lie algebra $\mathfrak{g}_2$ using a generalized Meinardus-typetheorem proved by Bridges, Brindle, Bringmann, and Franke.

Values and derivative values at nonpositive integers of generalized multiple Hurwitz zeta functions, applications to Witten zeta functions