The "old man" is a metaphor that refers to the person before he believes in Jesus. Paul describes our old sinful person as dying on the cross with Jesus when we believe in Jesus. You can translate this in an active form. Alternate translation: "our sinful person died on the cross with Jesus" (See: [[rc://en/ta/man/jit/figs-metaphor]] and [[rc://en/ta/man/jit/figs-activepassive]])
This can be stated in active form. Alternate translation: "sin should no longer enslave us" or "we should no longer be slaves to sin" (See: [[rc://en/ta/man/jit/figs-activepassive]])
Slavery to sin is a metaphor meaning having such a strong desire to sin that one is unable to stop himself from sinning. It is as if sin controls the person. Alternate translation: "we should no longer be controlled by sin" (See: [[rc://en/ta/man/jit/figs-metaphor]])