"Un día de mayo"

Yup, its just the way it's said in Spanish. En can mean in as well as on, or at. They prefer to say a day of may, a month of winter, a year of the 21st century, etc.

It sounded like un dia de majo to me

majo would sound like maho, if you catch my drift. And maho would sound like mao.

A more cosmopolitan way of pronouncing it would be somewhere between English y and English j, but some places like Spain it is substantially harder on the "y" sound and in others like Colombia it is strongly on the "j" sound. In general it's somewhere in between. This goes for y and for ll.