Quick answer
oír = to hear; the sound reaches you whether you want it or not.
escuchar = to listen, to pay attention on purpose.
When you cannot understand someone on the phone, the verb you need is oír, not escuchar.
Side by side
Te oigo pero no te escucho.I hear you but I am not listening to you — the clearest way to feel the difference.
Habla más alto, no te oigo.Speak up, I cannot hear you — a volume problem, so oír.
Escucha, tengo que decirte algo.Listen, I have to tell you something — asking for attention, so escuchar.
Memory trick
If the problem is volume or distance, it is oír. If the problem is attention, it is escuchar.
Typical mistakes
No te escucho, hay mucho ruido.
No te oigo, hay mucho ruido.
Noise stops the sound from reaching you, which is a hearing problem. Saying no te escucho accuses the other person of nothing — it says you are refusing to pay attention.
¿Has oído el nuevo disco?
¿Has escuchado el nuevo disco?
Sitting down with an album is deliberate attention, so escuchar. Oír would suggest it happened to be playing somewhere.
Check yourself
Bad phone line. You say: