There are MANY more than three strains of HPV that are oncogenic. The vaccines protect against two of the most virulent, but there are quite a few more that can cause cancer.
It’s estimated that 1 in 25 women will develop cervical dysplasia. Without treatment, about 30-50% of those will develop into cervical cancer. Source: http://www.thehpvtest.com/about-hpv/cervical-dysplasia-faqs/
The same HPVs that cause cervical cancer also cause other cancers, such as bladder, throat, anal, and penile cancers.
You are very correct. It has been long known, but well hidden that many lung cancers are also HPV caused, but because the meme is that smoking is the greatest "cause" that information has been all but hidden from view, and most often denied. It is also why HPV caused cervical cancer was kept so quiet for so long, it did not go along with the standard that it was smoking that caused the cancer.
The number of strains came from the CDC, take it up with them.
The vaccine only provides temporary protection. It has a significant rate of problems.