Question: I am trying to understand SHA uniqueness in simple terms.
For example let us assume there are only messages with maximum length of 4 bits (binery) in whole world. Number of possible messages with different lengths is 

* 2 for single bit length
* 2^2 for double bit length
* 2^3 for 3 bit length
* 2^4 for 4 bit length

that would be 2+4+8+16 = 30 (31 if we consider empty message 2^0 = 1)

Lets us consider SHA3(for example) with output length of 3bits (binery), so maximum possible number of digest are 8.
How can a digest be unique if we need to map 30 messages to 8, or why is it hard to find digest collision for 2 unique messages

Answer: 
"SHA3 which has digest length of 3bits"

I think this question is based on one bit misunderstanding. SHA-3 is a **family of hashes** that has the same output bit size as SHA-2. SHA-2 has bit sizes 224, 256, 384 or 512 for SHA-224, SHA-256, SHA-384 and SHA-512 respectively.

Of course, SHA-2 already took those identifiers, so SHA-3 will have SHA3-224, SHA3-256, SHA3-384 and SHA3-512. There were some proposals to use a different acronym, but those failed.

Still, SHA-3 hashes have near infinite input, so there will be many hashes that map to the same value. However, since it is not possible reverse any SHA-3 algorithm, it should be impossible to find a collision. That is, unless SHA-3 is broken, as it is not provably secure.
Any SHA3 variant will have digests with more than 100 bits. The terminology has probably confused you, because SHA256 has 256 bits, while SHA3 is considered the third generation of SHA algorithms (and does NOT have 3 bits of lenght). 

Generally speaking it's not hard to find a hash collision by brute-forcing (alas, it's time-consuming), what is difficult is producing a collision that is also meaningful in its context. For example, assume you have a source file for an important application, that hashes to a digest. If an attacker tried to alter the source file in a way to introduce a vulnerability, while also hashing to the same digest, he'd have to introduce a lot of random gibberish, making the attack obvious.