See, the definition of Indian Company u/s 2(26) tells; that Indian Company would be taken as any Company which is Reg. under Companies Act, 1956 and it INCLUDES:-
I. Companies which has been made before the 1956 (i.e even before the enactment of Company Act, 1956 itself) that would also be considered as company and that too Indian Company.
Logic- Because there was No "Companies Act, 1956" itself therefore No question of Companies being registered under Companies Act 1956.
II. Any Company which were Registered under specific act (obviously other than CA, 1956) which were enacted in state of J&K at any time.
Logic - Here also talking mainly about the Companies which were created through the specific acts of that special state because as you must know that most of the acts do not apply on J&K. But Companies Act, 1956 was extended to Whole of India including J&K therefore here talking about any company before CA, 1956 through any specific state law.
III. Any company which were created in the Union territory of Dadra And Nagar Haveli, Daman And Diu, and Puducherry before CA, 1956 or even after that would also be considered as Indian Company.
Logic- There are many states e.g Nagaland, Sikkim etc. where specific state company acts were also created but later on they all were abolished or merged into the CA, 1956. But in these 3 union territories CA,1956 were enacted with modified form as per their respective states needs (to attract the Companies etc there) and if any company registered under such Modified Act that would also be considered as Indian Company.
Note- GOA has been converted into state a long time ago i.e. way back in 1987. Now that is simply just a state like any other state.
VERY IMPORTANT NOTE:
For the Taxation purpose COMPANIES ARE CONSIDERED OF ONLY TWO TYPES;
1. Domestic Company (which includes all company other than foreign company and including INDIAN Company)
2. FOREIGN COMPANY (that is incorporated outside India)