I have had what sounds like a similar problem at my house. The house backs into a hill so the back part is essentially underground. Its concrete and concrete block. During heavy rain the water run off from the hill seeps through a couple of small holes in the concrete wall. This is because the waterproofing has failed and the drainage is not adequate (or has got blocked over time). Its a very common problem in my area (Titirangi).
The solution for me is to dig out the back and side of the house down to the foundations, apply appropriate water proofing (quite a lot of work here) then put in new drainage so it runs away from the house and direct to storm water drain. The cost to do this properly is approx $12 - $15k.
The cheap arse way to do it is to get a water proof product and apply to the inside of the wall and hope it works. Because this is my house I want it done properly.
I contacted some drainage companies and got quotes.