Let A¯ ℓ(n) be the number of overpartitions of n into parts not divisible by ℓ. In this paper, we prove that A¯ ℓ(n) is almost always divisible by pij if pi2ai≥ℓ, where j is a fixed positive integer and ℓ=p1a1p2a2⋯pmam with primes pi> 3. We obtain a Ramanujan-type congruence for A¯ 7 modulo 7. We also exhibit infinite families of congruences and multiplicative identities for A¯ 5(n).