Hi,
I have the same problem. Every time I update my website, spam links appear in the individual posts and in the blog roll links in the footer (https://www.billylane.com).
I’ve checked around and have ruled out most causes:
1. I’m on a Mac so it’s not a virus.
2. I have changed my passwords and it still happens.
3. You and I use different themes so it cannot be that.
4. The only plugin I have is Askimet so it cannot be hidden in there.
5. I have checked the majority of my files and cannot see any rogue code.
I am wondering if it may be my web host — may I ask who your website is hosted with?
I’m thankful that I don’t have too many posts (my blog is new), because it is quite an onerous task to remove them all. I worry my little brothers may see these links when they look at my blog.