Formaldehyde is indeed used for disinfection, but usually there is a subsequent procedure involving formaldehyde neutralization with $10\%$ to $25\%$ aqueous ammonia solution introduced (as a spray) at elevated temperatures. Ammonia reacts with formaldehyde producing water-soluble hexamine which, even though also has unpleasant smell of rotten fish, is then easily washed out from the fabric:
$$\ce{6 CH2O + 4 NH3 -> C6H12N4 + 6 H2O}$$
I'd suggest to wash the clothes at higher temperature ($\pu{40 .. 60 ^\circ C}$) as you would normally do, but adding some ammonia; afterwards, soak the clothes in cold water for a while (solubility of hexamine increases in cold water), wring out and air dry.
In some countries there are also ozone-chambers (basically a sealed wardrobe with an $\ce{O3}$ generator inside, offered by dry cleaning companies) where organic pollutants are oxidized; formaldehyde is no exception:
$$\ce{CH2O + 2 O3 -> CO2 + H2O + 2 O2}$$
Both vinegar and soda can also be used, though I'd think their effectiveness is going to be lower.