I've had to do similar here in Northern NSW. I find if it's fabric that can stand it, a super-hot soaking in Napisan overnight is good (and will also shift staining from the mould.) And then wash and rewash (I use just my normal detergent and also some white vinegar) until they smell ok again. Again, as hot as the fabric can take. Then get it really really dry before putting away/back on the couch. Cotton is generally much tougher than you think and can handle heat well.
Be aware that if you're doing lots of hot water and items that aren't often washed like curtains/couch covers, keep your colours separate to avoid dye running.
This isn't expert advice, but it's what I've done. And it seems to work so far.
I do agree with the suggestion of a dehumidifier as a future investment if you can afford one. It's making a huge difference in my house. And the electric ones work FAR better than any of the Damp Rid or similar products.