If someone with "XO" is one of the identical twins with the other twin as male, then what would the sex chromosome of the other twin be?
"XO" (an unpaired X chromosome) is characteristic of Turner syndrome.  The Wikipedia article https://en.wikipedia.org/wiki/Turner_syndrome provides a typical image - a woman with a fairly distinctive broadness of the neck.  The phenotype is described as female, though of course gender identity can be unpredictable for anyone.

For the other monozygotic twin to be phenotypically male, the most likely explanation is a Y chromosome - a Y chromosome that was lost in all or many of the cells of the XO woman.

A set of monozygotic twins with one XXY and one XO would be very surprising - in other words, with the twins differing by two chromosomes - would be very surprising.  But nothing is truly impossible in biology.  And ... this may be such a reference, but I didn't look at the full text to make sure: https://www.ncbi.nlm.nih.gov/pubmed/27315788