Can all type of songs be monetized with Content ID?

Actually no.

The following content types are not eligible for monetization, as per YouTube's terms of service: 

• Recordings containing (uncleared) samples
• Recordings based on free beats or any other publicly available sound files
• Compilations
• Music released under a Creative Commons license
• Recordings exclusively produced with sample libraries
• Public Domain recordings
• Cover songs
• Karaoke songs