Duane Hutchings was killed on Saturday, February 9.

A man has been charged with murder, and three others charged with aggravated home invasion and assault, following the fatal shooting of a father-of-five in Melbourne's south-east.

Duane Hutchings, 44, was found critically injured inside an Oakleigh East apartment on Clayton Road just before 5.30am on Saturday.

Relatives and friends said Mr Hutchings didn't live in the unit, but had been visiting friends when an argument broke out. He was shot, once, in the back of the head.