I had to self study them from different books to the best of my ability.
This sounds an awful lot like you simply researched topics that were relevant to your research. Under this definition, I have taken enough classes in my PhD/Postdoc/Professorship to have several extra degrees. Taking a course usually is reserved for actual courses you studied for and were examined on. It's generally expected that graduate students do what you described in order to be skilled researchers.
For grad students, the best way of proving you know something is to conduct research on the topic. If you have papers/manuscripts using finite element methods and non-linear continuum mechanics, then it's reasonable to assume that you are skilled in using these things, and listing them separately is redundant.
If you took some free online classes that may count: in that case you actually have some proof that you've taken these courses (say, a certificate of completion from Coursera or EdX).
Is there a way I can address the self-studied courses in my CV?
If you really insist, you could add them under the "skills" section (with your programming proficiencies and stuff like that). They will not carry much weight for general applications; however, if you are applying for a position that specifically asks for these skills (or that you know that the group's research interests focus on these topics) it may be worth mentioning. You can also say this in my application email.
When emailing my CV I'd say something like
"Dear Prof. X,
See below my attached application for your consideration. I would like to highlight that despite not having taken any formal courses on method A, I am proficient in finite element methods and non-linear continuum mechanics. Thus, I believe I would be a good fit to your group. "
do courses taken during graduate school carry weightage in shortlisting a candidate for a position if they are expected to teach exactly those courses too?
Not much. I am currently teaching classes I've never taken in my undergrad or graduate studies. If your studies are in the general topic that the department specializes in (e.g. a physics major applying to a physics department), there is an implicit expectation that you'll be able to teach a good chunk of classes, even if they're not in your area of specialization. Of course, no one wants you to teach stuff you're not good at, but things happen (manpower issues, someone is sick or leaves abruptly etc.). People often end teaching statements with a list of courses they're willing to teach - just list those you're happy teaching.