A technician will typically test combustion and venting, check the circulators, expansion tank, and relief valve, and look at how hot water is produced. On a coil boiler that means the coil, the mixing valve, and the boiler's temperature settings. With an indirect tank, expect checks of its zone valve or pump, its thermostat, and the tank itself.
For replacement, oil work goes through the Fire Department's oil burner permit and gas work through the Building Department, which schedules inspections through its office staff. If a coil boiler is being replaced, ask whether the new setup will use an indirect tank, a combination boiler, or a separate water heater.
An older Stoughton basement may be cramped or have low beams. Mention access when you call, since a boiler and tank swap may involve moving two large appliances.