This paper pursues positive characteristic analogues of the results of Furusho, Komori, Matsumoto and Tsumura on p-adic multiple L-functions. We consider ∞-adic and v-adic multiple zeta functions concerned by Anglès, Ngo Dac and Tavares Ribeiro. Our main results in this paper consist of:(1) integral expressions of special values of ∞-adic multiple zeta functions, (2) integral expression of v-adic multiple zeta functions themselves similar to those of p-adic multiple L-functions, (3) Kummer-type congruence for the special values of v-adic multiple zeta functions at integers (4) relationships between special values of ∞-adic and those of v-adic multipe zeta functions at negative integers and (5) orthognal properties of multiple zeta functions and multiple zeta star functions.