The mockingbird represents true goodness and purity. Tom Robinson is one example of a human "mockingbird". He stands accused of raping and beating Mayella Ewell, but is innocent of the charges. The town commits the ultimate sin by finding him guilty and sentencing him to death. In effect, they have killed a mockingbird. Boo Radley is another example of a human "mockingbird". He has spent his entire life as a prisoner of his own home because his father was overzealous in punishing him for a childhood mistake. Boo Radley observes the world around him, causing no harm to anyone, and then saves Jem and Scout's lives when Bob Ewell attacks. The sheriff determines that Ewell's death will be ruled an accident to avoid forcing Boo to go to trial, even though Boo killed him to protect the children. Atticus agrees, and wants to make sure Scout understands why this little white lie must be told. She replies saying of course she understands, putting Boo on trial and in the public sphere would be like killing a mockingbird. The mockingbird represents true goodness and innocence that should always be protected.
I'm not sure which character or characters I would consider blue-jays. I'll have to think about that further.