Immune to backlink blasts?

One of my websites is ~6 years old, pr3 and has roughly ~1000 legitimate backlinks that have been generated over the years.
I've never performed any type of SEO on this particular site as it currently sits in the #2 position for 5 big keywords, and the only site beating it is an EMD that also links to my site.
Recently I was checking the backlink profile of my website and I noticed I have ~80000 backlinks from AA blogs that consist of keywords like 'viagra', 'buy viagra', 'online gambling' as well as a handful that relate to mobile phones and SMS.
Now my question is why am I experience no negative effects in SERP's from these blasts?

To answer your question about why you have no negative effects in SERPS from these blasts is because it takes time for search engines to notice blasts like this. Usually 1 to 4 weeks.

If I were you take action before you lose rankings. Go to google webmaster tools, download all the links, filter out the negative links and disavow them. That will help and possible prevent a SERP downgrade.

Chances are google picked up on the blast and knows your site is not at all related to Viagra. Basically they take the anchor text and match it to your onsite test. Obovusly they know which keywords are spammed the most.

Now my question is why am I experience no negative effects in SERP's from these blasts?

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Because negative SEO campaigns that target your primary keywords is what will do you the most harm. Be grateful they did not do that (yet).

I should clarify, this has been done to my site before with my main keyword, but much smaller (5000-10000), I disavowed all of those links the first time because I was worried about being penalised, but even then the links were live for ~3 months before I took any action and i saw no change in SERP's
I have absolutely no competitors, so I can't understand why anyone is actually trying to NSEO my site.