what's the best way to both kill and repel cockroaches?

[Jackmannii]

For you natural remedy types, the fruit of the osage orange tree (or the oil extracted from it) is said to repel cockroaches.

While the linked article says the stuff isn’t actually lethal to roaches, you could kill the ones that hang around by whacking them with the heavy fruit.*

*Osage oranges weigh enough that they could cause fatalities to humans when dropping from the tree in fall.

[Chronos]

While I suppose it’s possible that some human somewhere has been killed by a falling osage orange, they’re not all that big, nor all that hard, nor are their trees particularly tall.