Can Istanbul be reached by ferry services from Athens?

There are no ferries between Athens/Piraeus and Istanbul.

Take the bus or plane. Flying would be faster but more expensive.

There used to be a train going to Istanbul......not sure if it's still running.

No such service. Only as part of a cruise with one or more Greek Islands in the between.

The best way to do so is by air and there are such very cheap fares for it. Search any on-line ticket selling company.

there is direct ferrie trips from the Greek Islands into Turkey...not into Instanbul but you could make your way there from the following

Chios-Çeşme

Kos-Bodrum

Kos-Bodrum

Lesvos-Dikili

Lesvos-Foça

Lesvos-Ayvalık

Rhode-Bodrum

by doing this you'll see beautiful Greek Islands as well as lovely Turkey

By plane