The DMCA law only refers to take-down notices, not strikes.
A DMCA take-down notice is a formal, written request to take down and remove allegedly infringing content (i.e. content that is not licensed for use by the content creator) and can only be issued by the copyrights holder(s) or someone who have the right to represent the interests of the copyrights holder(s). These take-downs are sent from the copyrights holders to the content creator or the representative platform or OSP (Online Service Provider).
There can by many copyrights holders for one piece of media -- especially when music or video is involved. Music is licensed mainly on two main areas: mechanical and composition. Sometimes the copyrights holders are the same people/groups, but not always.
A "DMCA strike" or "Copyright strike" is an infraction or warning sent to the content create by the platform (or OSP) after they receive a DMCA take-down notice from the copyrights holder. The law does not specify anything about strikes -- these are platform specific rules and guidelines.
To learn more about the DMCA process and how it works, read this.