Why are DNG files 4 to 6 times larger than OM systems ORF raw files?

Totally to be expected as these are linear DNG:

http://www.barrypearson.co.uk/articles/dng/linear.htm

Just as a single-channel grayscale document is 1/3rd the size of an RGB document (three channels). 

Linear DNG isn't 'as raw' as the original; it is partially processed. 

This will sort of be redundant with what Richard explained. My understanding is that the AI-processed files are demosaiced into a Linear DNG file. So it goes from only having to store one channel of data (raw mosaic) to having to store three channels (demosaiced into RGB). Three channels of data is a lot bigger file than one channel.

This is not new, the earlier AI-powered features in the same Enhance dialog box (Raw Details and Super Resolution) also produced their results as a much larger demosaiced RGB stored in a linear DNG file. All of them take the raw data, do their thing, and, being totally unable to save the results back to the read-only raw file and having nowhere else to put them, save them in that much larger three-channel RGB file.

It’s sort of similar to converting a raw file to a TIFF or Photoshop format file: A single channel raw file must expand to a three-channel RGB file to be editable in a non-raw editor such as Photoshop, so TIFF and Photoshop versions are always much larger files than the original raw file.

But there is hope. In the Adobe engineering article about AI Denoise (Denoise Demystified), they say:

We’d like to support additional file formats and combine Denoise with Super Resolution. We’re even looking into ways to speed up the workflow by not needing to make a new DNG file. It’s a very exciting time, and you can expect us to continue making big strides forward…

The fact that Adobe thought it was safe to say that suggests they might have a way to do it. If Adobe can pull that off, allowing us to perform AI without the DNG copy, it will become much more practical to work with AI Denoise at scale without consuming large amounts of storage space.

So the answer to the question about saving storage space might be “Wait for a future update.”

I don't think so, except as to how many images you do this for.

There are circumstantial differences of lossless compression method, of what else besides picture data may be stored in the file, of the number of binary 'bits' expressing each value in the picture data (whether using integer or floating point format), plus, different data may prove more or less compressible.

But the greatest efficiency - so far as file size in particular - of a Raw file from a (typical) Bayer filtered sensor vs other formats, is that the former holds only one value contributing towards each eventual pixel. As if it were monochrome, loosely speaking.

As far as I can make out, the semiprocessed DNG arising from Enhance holds a 'red', a 'green' and a 'blue' component value contributing towards each eventual pixel.