Air Carrier Captain reported an intermittent fume event during a two segment out and back flight. Flight crew submitted an APU logbook discrepancy after first segment which Maintenance signed off. Several crew members reported experiencing lingering physiological symptoms.

Narrative

Showed up to work with no illness or headache. At engine starts I smelled chemical fumes (magic marker/dry erase pen). After engine starts I shut down the APU and these fumes disappeared so I figured they were transient. In climb out through a marine layer of clouds; I smelled it again and got a call from the aft galley Flight Attendants saying they smelled something from their overhead air gaspers. One described it as a burnt sugar smell and the other as a strong window washing chemical smell. We looked at the FOM and determined it was a Level 1 transient odor. On Taxi in at ZZZ1 after starting the APU and bringing on the bleed air; I smelled the same chemical smell. Got a call from Flight Attendant right away from the aft galley. Turned off the APU and taxied to the gate. Called Maintenance and wrote up Level 1 fume/odor event in logbook. (Later realized it was more of a Level 2 since multiple crew sensed it and different times on the flight). Had the crew leave the plane and get fresh air in the terminal while Maintenance checked it out. Myself and another Flight Attendant from the aft had strong headaches. Spoke to the Duty Chief Pilot Name about the event. Took ibuprofen for headache and flight attendant took acetaminophen for hers. Returned to the aircraft after about an hour and did not smell that fume/odor. Maintenance signed off the APU and cleared the aircraft to fly and we returned to ZZZ on Aircraft X. Had a headache the rest of the day and when I got home it was more of a migraine. Went to bed extremely early to sleep it off. Had a headache the following couple days plus fatigue and flu-like symptoms. Called Medlink to talk about my symptoms and get their recommendations on what to look out for.