I am on probation for a misdemeanour and will be traveling to England, Wales, Ireland and Scotland this August. I have permission to travel from the PO. Will I need permission from each of the countries to enter?

Yes, permission to travel from PO, passport and visa to enter each country

Yes, permission to travel from PO, passport and visa to enter each country

With the exception if Ireland, it's all in the UK. Does OP need visas for each country, or just an Ireland and a UK visa?

There's one UK wide visa as the individual nations do not issue their own.
This excludes Southern Ireland as that is a separate country.