Sometimes poison really is the only way forward - I would get a professional in as they have access to more effective poisons.
Make sure its the right type and format for the location - no little portable packets of poison (designed to be a ratty/mousy takeaway, to be taken home and shared with family) around pets for instance as these are easily dropped by a startled rodent and left for pet/child to pick up.
I like the wax blocks with a hole in, they can be wired onto something solid or locked in a bait station so put in places kids and pets can't get at, and they're waterproof.
The downside of these is they are less palatable and won't be chosen if there are nicer things around - rodents are not thick!
I would also only ever go for a poison that uses Bitrex, and a mouth staining dye, (but be aware, some people cannot taste Bitrex... my Mum couldn't taste it when the rep brought round sweeties with Bitrex in to show pest controllers how strong it was... and she was a pest controller so whilst unlikely to eat poison on purpose, at a higher risk of accidentally ingesting it. Dogs can't taste it either I think).
Otherwise - block up likely access points, remove clutter from the house and garden that is providing shelter and remove food sources as much as possible.
Trapping is useful to tell you there is a problem and where and for long term monitoring, but poison in most situations is the only actual longer term solution.