Are collisions possible on the output of Blowfish? I'm using the Blowfish block cipher to encrypt messages of 64 bit without using any block cipher mode of operation. Can I still have a collision?

I'm asking this to understand if Blowfish is susceptible to the birthday attack when used on plaintexts of 64 bit.
No, you cannot, unless you have repeated messages, or use different keys. A block cipher such as Blowfish is a keyed random permutation or bijective mapping.

That means for each key any plaintext block is mapped to exactly one ciphertext block during encryption, and the ciphertext block is mapped to that particular plaintext block during decryption.

For different keys there are different mappings. So if you mix keys you may get a collision.