The group from the Tasman Islands crossed over by boat to the Malaita Outer Islands on Boxing Day, allegedly to purchase the local homebrew called Kaleve.
They were arrested by police and screened by medical authorities in the outer islands before being transported to the capital.
In Honiara, they were further screened then released to police after testing negative for Covid-19.
Three 19-year-olds and a 34-year-old have been charged with illegal entry by a non-citizens under Covid-19 state of public emergency regulation.
The group have been remanded at Rove Correctional Facility, due back in the Honiara Central Magistrates court this Friday.
Police ask public for info on dead body at Noro
In Solomon Islands' Western Province, police have called on members of the public at Noro and surrounding communities to help identify the dead body of an adult male person discovered floating at sea.
The body was recovered in waters of the Kokosu area off Noro Township this morning.
Supervising Provincial Police Commander, Inspector Wilken Miriki, said police have allowed members of the public to view the body for identification but so far no one had been able to identify it.
"An inquiry file has been opened and I appeal to anyone who may have information to assist police."
"It is a sad incident and my condolence to the family members of the deceased as we try to identify the dead body. I call on anyone whose relative has not turned up at home since last week to come and identify the body."
Police at Noro are also seeking to engage a doctor to examine the dead body to assist the investigation into the possible cause of death.