My previous advisor published a paper with my work and did not include me as a coauthor or give an acknowledgement. How to continue? During my undergraduate degree I was involved in a research project under a new, young professor. I was much more involved than a typical undergrad researcher (at least from what I have seen during the past year in a PhD program); I was a major contributor in developing the theory and solution codes, and I was a first author on one paper and a coauthor on another during that time. A long story short, the professor had a really bad attitude and had no problem making enemies. Within two years he was gone (rumors that he was forced out) from his first professorship, which is a top 10 engineering school to a much less prestigious one. I graduated at the same time and started my PhD at another school. 

An extremely long story short, we had a falling out not long after because I had had to shift my priorities to my PhD as any reasonable person would; however, I had agreed to keep working with him during my spare time as we were nearing in on one last paper. In short, he sent me some pretty disrespectful emails, and any time I tried to defend myself in any way, he took it as inappropriate. I tried my best to remain professional and respectful, and in my opinion I succeeded with that. I just decided I had my whole future ahead of me under a much more prestigious advisor and one relatively low impact paper was not going to mean much. So I told him that I could no longer contribute to the project.

A few days ago, I see that he published the paper we were working on. Unsurprisingly, I was not included as a coauthor or acknowledged in any way, though he did cite our previous papers. What was really bizarre was that he included as a coauthor another undergrad researcher who was less involved in the project. This guy happens to be my good friend, so I know he hasn't worked on it at all in the last year. To make things even fishier, my friend didn't even know he was going to release a paper nor was he ever notified that he was going to be a coauthor. I was the one that told him about it, and he was completely shocked.

The paper contained nothing new from what I had done, and the results were most definitely produced with the subroutine I wrote. Also, the wording was very very similar (not quite word for word) to what I had written in the past. The figures (containing conceptual designs) had been reproduced directly from my own unpublished ideas. 

I am wondering just how unethical this is, if at all. I know typically undergrads might not contribute much, but I genuinely feel that I was the major contributor of this work. I even secured two external fellowships to fund the project. I have developed a lot of close contacts that are in high positions that I am confident would support me in a dispute, not to mention his reputation in the community isn't the greatest. I am just trying to decide if its even worth it and what route to take. Should I just let it go or am I in a position to act? I haven't contacted him yet since he will surely try to sabotage me in some way, which I am not that worried about; I really just don't know if I want to deal with it.

I am just looking for some thoughts, so I can approach this as unbiasedly as possible. Thanks a lot for your time.
Contact the editor responsible. Talk nicely to him, and ask him how to proceed.

Since a friend of yours is included as coauthor without his knowledge,  you have quite some leeway. If one of the authors asks for the paper to be withdrawn because of incorrect attribution, this may very well happen. Such behavior is considered scientific misconduct.

Also many universities will have an office responsible for processing with plagiarism and other scientific misconduct, and may be able to assist you with drafting such emails.