Can an engineering graduate get back to technical role after having experience in audit firm?

When you are attending interview for a technical position you definitely will be questioned for the gap period. If you tell them your serving with an auditor office, there are minimum chances of understanding your situation. So it is better to tell them that you engaged yourselves on odd jobs due to unemployment. Though it is against morality it is inevitable.

If you join in an auditing company for a commercial role, that experience will not be of any use for you to get a job in the technical line. So it will not be a correct job for you. You have to think twice before joining.
But you need a job immediately. A bird in the hand worth two in the bush. If you leave this chance, you may not get the chance again.
If I were you, I prefer joining in the job for which I got selected. Once joined there I will be getting some money and I need not worry about the daily expenses and family expenses. Then we have to think about the career.
While working here apply for some other job which is in your field and join the same by resigning to this job. The other way is to think about becoming a surveyor and do loss assessments for various insurance companies as a free lancer.

There are several points to be considered at the present moment and the important considerations are as follows -
1) Though basically, you are a graduate in Electrical Engineering but you are not coming across a suitable job connected with your area.
2) You are unemployed currently making you tensed how to manage your your financial expense for both you and your family. Your acceptance for the job of Audit can provide you a stable income for both you and your family.
3) No assignment is less important. Negativity should not set in due to your present phase.
Graduate in Engineering has given you enough wisdom to analyse the situation in a more realistic way, hence enjoy the assignment at present.
4) You should make an effective resume indicating your extra curricular activities in different areas while studying in your college.
Look out for some vacancy in some electrical firms both in the medium and the larger one either through the paper advertisement or some consultants such as Naukari.com, Jobs Monster, Times of India.com so as to get a job in your area in the oppurtune moment without leaving the audit job till the job in your area is finally confirmed.
BHEL is a public undertaking recruiting graduate engineers in each stream. You can make an enquiry from the said organisation.
The employers of some of organisations are intelligent enough to assess your potential in the process of interview. Hence give up your negativity and brush up your knowledge in your own stream with an optimistic note. Ultimately, you are to land a job in your own area ultimately.

One cannot wait indefinitely for a job in one's core competence area. When it comes to the question of a livelihood, there is no distinguishing between the two jobs. I would suggest to join the said Audit related job at an earliest and then in your part time you can plan for your future aspirations. One can think of increasing ones skill base by acquiring some certifications in the area of interest and then keep a watch on the jo portals to see if anything of interest is popping up there. In case one gets a suitable position then one can apply and switch the present Audit job with that.
I have seen many young engineering graduates who are doing very good work in non core areas and are very successful in that. Many are working as material acquisition managers and with the engineering background their performance is quite good. So one should not shy of from a particular job because one is not getting job in ones core area.
Today the job market is very tough and going through a big shortage of jobs everywhere. In such a situation we are not the choosers and have to manage with the available ones. At the same time it is necessary to do necessary efforts to increase our skills in newer areas and keep a watch on the job portals so that we can take benefit of any opportunity that strikes on our ways.

You are a B.Tech EE and you have working experience without any experience certificate. But you were fired from two companies. It may create a problem for you if you show your working experience of these two companies. So you are still like a fresher.
Now, being a jobless you want to click this opportunity. Since you don't have any degree or experience in audit , so you don't have a good future in this field but you may join it as long as you don't get suitable job which suits your B.Tech degree. You may join job portals and keep on searching a suitable job.
Also check Job Section of ISC here
https://www.indiastudychannel.com/jobs/

To switch from your main specialized area is always risky but in your case, you need a job at the earliest. So, I suggest you join it and at least start working. There are below-mentioned possibilities for your future-
1. You may find the auditing work more interesting and rewarding and may change your views about going back to the technical field.

2. By the time you are working in that audit firm, keep looking and trying for jobs in a technical field. Learn closely about their requirements and then only apply.

3. You may need to pursue some short-term training or refreshment course before entering back into the technical field. So, you should prepare yourself for that also.

You should request your previous employers for an experience letter as it is your right.
You did not mention the reasons for which you got fired from your last 2 jobs. It is advised that you must not mention these jobs in your future interviews if you do not have any experience letters for the same.