The lights on the wings that were flashing are so-called STROBE lights taht are being switched on when entereing the runway for takeoff and switched off when leaving the runway but remain illuminated during the complete flight. They are designed as anti-collision lights.

The red flashing light is a so-called rotating beacon or anti-collision light that has to be illuminated before the engines are being started and shut off after the engines stopped. They are for collision avoidance as well as warning sign on the ground that the engines are running

Additionally, you will find navigation lights, on the left wing a red light, on the right wing a green light and at the tail a white light. They are designed to see in which direction an aircraft (or boat as well) is travelling at night/in bad weather. Commercial airliners however use them for the full duration of the flight.

Since all these lights are standard (strobe lights are however not mandatory on small airplanes like a Cessna 172 or Piper PA28, but still often used), you should be able to see them every time you have an airplane passing over you....