How do Filipinos speak English? They all sound like strong accents. Is it a big obstacle to communicate with foreigners after learning English from Filipinos?

You do have an accent. Do you learn from ordinary Filipinos, or from Filipinos who specialize in teaching English? Just like China, there are some people who speak perfect English. Listen to your accent before you learn from others. If you really learn Filipino English, you must have an accent, and you will know it when you communicate with Europeans and Americans, but generally you will not discriminate. You may just think that you are Filipino and there will be no obstacles in communication.