How OR gates are garbled in recent optimizations techniques like free XOR, Half Gates?
Usually, only AND gates and XOR gates are considered in garbled circuit schemes, because they form a complete basis for boolean circuit - id est, any boolean circuit can be written only with XOR gates and AND gates. In particular, you can implement an OR gate with a single AND gate and only XOR gates, using the fact that $a \text{ OR } b = \text{not }((\text{not } a) \text{ AND } (\text{not } b))$, and $\text{not } x = 1 \text{ XOR } x$. Therefore, with the latest scheme which garbles AND gates with two ciphertexts, and where XOR gates are for free, garbling an OR gate uses only two ciphertexts, exactly as an AND gate.