He's clearly not invincible since he's dead.
Furthermore, Susanoo has at least three weaknesses. 1. The base does not protect the user. This leaves the user vulnerable to ground/underground attacks; 2. Susanoo isn't very mobile. Any attacks that are strong enough to move Susanoo, leave the user vulnerable. This also leaves Susanoo vulnerable to area-based attacks; 3. Even Susanoo has its limits. In other words, any attack that is strong enough, can completely destroy Susanoo and leave the user vulnerable. Examples of such attacks are Kirin and Hashirama's jutsu that he used against Madara.
Furthermore, Susanoo has at least three weaknesses. 1. The base does not protect the user. This leaves the user vulnerable to ground/underground attacks; 2. Susanoo isn't very mobile. Any attacks that are strong enough to move Susanoo, leave the user vulnerable. This also leaves Susanoo vulnerable to area-based attacks; 3. Even Susanoo has its limits. In other words, any attack that is strong enough, can completely destroy Susanoo and leave the user vulnerable. Examples of such attacks are Kirin and Hashirama's jutsu that he used against Madara.