"meejum" is phonetic rendering of"medium". It was a (semi-official?) measure of beer between a "glass" (half pint) and a pint. I believe it was common in Dublin at one stage, but is now almost extinct. Reminds me that at one point in the price/volume ratio for beer, there was a fashion for selling it in half-litres because it kept the price below a pound! Not for long, though!

Regards