We have mice!

So I've suspected for a few days hearing random scratching sounds. And tonight after hearing squeaking and finding droppings in my kitchen I'm now certain.
So. Help! I need to address the problem but how?
I own a cinnamon gcc who's cage is in the main living area with us. The quickest way is to put the traps and poisons down but I have reservations about keeping something potentially poisonous in the same room as her.
Can they give off fumes? Can it be dangerous to her?
I've put off putting preventative flea drops on the dog too so if anyone knows of bird safe products there too that would also help.
I am all for non kill traps too but I think we have more numbers than that solution can cope with quickly.

Call an exterminator. Find one that doesn't use poisons (just traps.) We went that route with good success.

I know they are pretty cruel, but mice are a worry for your birds, so I would not hesitate to put down glue traps... the mice will be drawn to the food and can cause serious bites to feet and legs. The traps are a bit inhumane, but bird safety first.... make sure the traps are up or removed if ur bird is out of cage.

Sorry to anyone upset by the suggestion, but we have a cockatiel missing tip of a nail from a pet rodent bite..., needless to say, no more pet rats for us!!

I had mice once. I fed them for a week under the T.V. In a small space. Then, I switched it with poison. The birds couldn't reach it. In a few days, no more mice. Glue traps are horrific, and it takes a while for the mice to die.

Glue traps are horrible, agreed.... but I don't have scented candles or potpourri anywhere, no way putting poison out. Hell I won't allow bug spray even if birds removed! Just my opinion, but if its Ivorys feet or PC treatment of a mouse are my options, I will buy the wood to build the stake on which to flame me...

There are two kinds of humane mousetraps and I'd go with either one of them. The first is a longish plastic box with about a 120º bend in the middle and a trap door at one end. You put bait in the farthest end and, when the mouse goes in to eat it, the trap door shuts and mouse is imprisoned. You can then release it outdoors or into a bucket or wherever.

The second is a larger wire box-shaped trap with a cone let into the top. You put bait in it and the mouse must push through the cone to get in. He can't get out again and so is trapped. His distress calls will usually entice his family and friends to join him and so you usually catch many or most of a colony this way.

My personal philosophy is that I could never cause deliberate pain or suffering to an animal. I know mice are pests, but we have eagles, hawks and falcons who really appreciate their existence. Spring traps are foul, horrible things and even the thought of a glue trap makes my blood run cold.

I have used humane traps for years. If I'm only catching one or two mice, then I release them into the drain at the end of our street. If there's a plague on and I'm catching lots, then I release them into a lidded, ventilated bucket and then relocate them en masse into the swamp on the Minmi Road.

Funny story: a friend once remarked that the mice were finding their way back to my house every time I released them. Since mice can only see six inches in front of themselves and smell not much more, I doubted it, but decided to test the theory. As I took each mouse from the humane trap, I dobbed a bit of pink nail polish on it.

Five nights later, I caught a pink-spotted mouse!

That mouse had travelled roughly half a kilometre from where I had released him! I christened him Vasco da Gama and took him all the way to Minmi to let him go the second time. Never saw him again, nor any of his spotty little friends.

Thanks for the tips. I don't know how big a problem it is as I hear them and see evidence, but don't see them. I don't know if we're talking a couple or dozens of them. I thought it was safe to say that by the time you notice them, you probably already have an infestation?
My partner wants to put down poison and do the job quick. I am very reluctant. Both as an animal lover and because I don't want poison in the same room as my pets. I'd rather catch and release them into the wild. There is a cemetary/nature reserve not far away that would be perfect.
I think I'll buy the non kill catch traps and see if our problem lessens.