I have somehow completed my PhD without having the required theoretical understanding of my field. Can I have an academic career? I have an undergrad in mechanical engineering. My Masters, PhD was in Mechanical too. However, I have never been academically strong (grades were majorly C and B+). I had to retake advanced mathematics, continuum mechanics and Finite element analysis course during my undergrad as I had flunked the courses.

However, I always enjoyed the field of computational mechanics, how materials behave is something I enjoy thinking about. I pursued the field in my Masters and PhD, inspite of not taking any grad level course during the programmes. My committee never instructed me to take the courses, I thought self study would suffice.

I have a PhD in application of computational mechanics, I have 3 first authored papers in materials science journals, not mathematics intensive journals. I am worried about my future in the field.
I am continuing with a postdoc under my PhD advisor for a year and am searching for other positions.

I shouldn't have pursued higher studies, atleast not in a field I have theoretical deficiency. I still love my field, but I am still afraid of the theoretical papers in my field. My work (application focused) is not mathematically intensive and is pretty straightforward. I can argue that given a direction, one doesn't need a masters or PhD to do what I do.

I know, there won't be anyone who had experiences similar to mine. It is always expected that people go for highers studies in subjects they are good in. I did the other way round. What should be my course of action now to have a potential academic career? I think I am up for a dissappointing career outcome, but still I want to give it a try.
This is a pretty solid case of Imposter Syndrome, I think. Yes, lots of other people have experienced it. Part of it is the letdown after completing a degree, perhaps. Part of it is the realization that your field is very wide and no one can really grok all of it. 

But you seem to be able to function pretty well in your field. Thesis? Check. Papers? Check. Specialization? Well, yes, of course. Doctorates are like that. 

The test of it, is whether you can get a suitable position. If you don't fall in to depression and sabotage your own applications then I doubt that there are any real barriers. The research you love is valued by academia. Do that. 

If you are still connected to the university, they probably have a counseling office where there is someone familiar with these sorts of feelings and can give you some professional advice. 



As to your grades, they were apparently strong enough that people let you continue your education to the end. No one will care much anymore about them. They can be a poor, or at least imperfect, surrogate for measuring knowledge in any case.