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The problem is known in the literature as private function evaluation (PFE). A sender has input (a function) $f$; a receiver has input $x$, and only the receiver learns $f(x)$. If you are willing to leak the topology of a circuit that computes $f$ (but not the identity of the gates), then using classical garbled circuits / Yao's protocol will work. These ...

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There's a new really simple OT protocol based on DH. It's even practical. Watch this video. For the paper and source code, go here.

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Kolesnikov & Kumaresan defined a primitive called "string select OT" which basically covers your setting but with a database of 2 items. Sender has $x^1, y^1, x^2, y^2$. Receiver has $x^*$. If $x^* = x^i$ then the receiver learns the corresponding $y^i$. I think a generalization of their protocol would work, at the cost of $n$ 1-out-of-2 string OTs ...

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