All contracts can be written or oral. Parties, however, usually prefer written to oral, as it means you have sufficient documentary evidence to prove your claims. This, however, does not mean that oral contracts cannot be proved. However, in order to prove oral contracts, heavy burden lies on the plaintiff (you) alone. In this case, as no contractual agreement was signed, the burden to prove the existence of the contract lies solely on you.
You have to prove it via witnesses, actions of the company- its decision to provide permanent status to all other employees in your batch; except you and constantly promising you the status if a permanent employee etc.
There are few concepts you need to know, in your case:
"Unconscionable bargain", which means that - party with weaker bargaining power in actuality enjoys no opportunity to bargain and has no alternative between accepting the offer of the other party or reject it. In your case, you were left with no option but to believe that eventually, your employers will end up offering you a permanent post. This belief and lack of other alternatives mean that you have been stuck in a case of "unconscionable bargain" in such a contractual scenario.
"Permanent employee"- more than the designation that they offered you, we need to look into the nature of your job to support your claims. You have been given the work of maintenance of accounts and taxation work. This is not some manual or clerical work that any person could do, as it requires a certain level of skills and knowledge. Furthermore, if you have been employed in some capacity for a period of 6 months or more and the vacancy that you have filled up is a “clear” one, i.e. your job designation and tasks assigned are clear, then it means that you are a permanent employee.
All such administrative decisions are based on the concept of "Equity"- you have to follow similar rules for similar people. In this case, your claims that others in temporary capacity who were employed alongside you were provided permanent employment, and they used "political contacts" for the same. This means that there was no such rule or guideline followed. rather, it is a case of nepotism.
Thus, I suggest that you first file a case in the consumer court
, and do that as soon as possible to avoid being debarred by limitation period.
IF case your case is dismissed in the consumer court, you can approach the High Court and seek permanent status as an employee with possible monetary allowances for your upgradation as a permanent employee being unfairly delayed over such a long period of time.
Sources referred to - https://indiankanoon.org/doc/1651662/
Central Inland Water ... vs Brojo Nath Ganguly & Anr on 6 April, 1986
Equivalent citations: 1986 AIR 1571, 1986 SCR (2) 278, available at https://indiankanoon.org/doc/477313/
Dwarika Prasad Tiwari vs M.P. State Road Transport ... on 13 September, 2001, Appeal (civil) 636 of 1998, available at https://indiankanoon.org/doc/184978896/