Congruences modulo powers of 2 for t-colored overpartitions

Let (p) over bar (-t)(n) count the number of t-colored overpartition of n, with t=5, 7, 11 and 13. We find several infinite families of congruences modulo 16 and 32 for (p) over bar (-t)(n). For example, For each alpha, beta and gamma >= 0, (p) over bar (-11)(8 . 3(4 alpha) . 5(2 beta+2) . 7(2 gamma)n + t(5) . 3(4 alpha) . 5(2 beta+1) . 7(2 gamma)) equivalent to 0(mod 32), where t(5) is an element of {7, 23, 31, 39}.