Inteal desktop ODD as exteal to laptop

There is no difference between Optical Drive SATA devices and spinning rust SATA. If you have a working cable from an eSATA port to SAta then you can use this just fine for your buer.

Also will there be enough power from the laptop?

You really should use an exteal power supply. eSATA does not provide any power, so you would need that anyway. There are 'powered eSATA' connectors which provide limited power. Usually enough to spin a 2½ inch drive. But desktop CD/DVD writers draw much more.

(I never had a BR writer, so I am assuming those also draw a lot more).

There should be no problem with a case which you can also use to power regular 3½ inch harddrives though.

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