That's not really an engine consideration, but dependent on the hardware you run on. On most platforms halving your texture simply halves the memory requirements without any other influence.
However some mobile chips, most notably the powerVR GPUs in most (if not all) iOS devices, do not support non-square textures at all. In those cases Unreal will automatically add padding to the file to make it square, resulting in the same memory load for all those variations you just mentioned. Other engines might handle this slightly differently, but the constraints are the same.
TL;DR: Only use square textures for mobile, use whatever you like on everything else.
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However some mobile chips, most notably the powerVR GPUs in most (if not all) iOS devices, do not support non-square textures at all. In those cases Unreal will automatically add padding to the file to make it square, resulting in the same memory load for all those variations you just mentioned. Other engines might handle this slightly differently, but the constraints are the same.
TL;DR: Only use square textures for mobile, use whatever you like on everything else.