My company started 3 years ago.
My company was founded 3 years ago.
but what about
My company is 3 years old., or My company is 3 years.?
Probably both are wrong.
But is there any other way of saying the age of a company or an object (ex: this table is two years old' also sounds awkward) in the same fashion of a person's age?
My company is 3 years old
is absolutely correct. [noun] is [number] [units] old is the way to describe the age of people, objects, institutions, whatever. (It's a little strange to use units smaller than a day, but that's only because we don't usually talk about age on such a small scale; it is nevertheless possible and correct to do so)
The temple of Bal Shamin in Palmyra was almost twenty centuries old when it was destroyed by ISIL in August 2015.
The New York Stock Exchange is 198 years old.
My daughter is just three weeks old.
Using this format usually implies that the object's exact age is strictly greater than the specified time. A child who was born seven years and eleven months ago is almost eight years old.
But for old things, and especially where the time we're discussing has only one significant figure, you're allowed to fudge the numbers. If someone said the NYSE was two hundred years old, they wouldn't be misusing the expression, even though its actual age is just 198.
This sentence:
X is three years old.
works fine in English, no matter if X is living or inanimate, concrete or abstract:
My sister is three years old.
My cat Gracie is three years old.
My red car is three years old.
My pizza business is three years old.
The Republic of Gremrovia is three years old.
All of those are grammatical; all are normal, idiomatic speech.
As for:
X is 3 years.
That one doesn't quite work. We can make that work, though, if we change to verb "is" to something else (such as "has existed" or "has been around"), and use "three years" at the end of a prepositional phrase. For example, any of these would be fine:
My cat has been with me for three years.
My restaurant has been open for three years.
But maybe the best way to talk about the age of something is to employ the word ago:
My sister was born three years ago.
My cat moved in with me three years ago.
I bought that red car three years ago.
My pizzeria opened three years ago.
The Republic of Gremrovia proclaimed its independence three years ago.
"My company is 3 years." is wrong. Your company cannot exist as a period of time, barring some new extremely weird field of science.
However, all of the other examples you posted are correct and valid. "My company is 3 years old" isn't very formal, so I would use "My company was founded 3 years ago" instead if I were trying to sound professional. Other than that, they're both perfectly fine.
