If you are a sweaty person, then your bare armpits shouldn't have contact with either the jacket or the dress. If you buy sleeveless dresses you need to always wear a blouse underneath.
I would wash the dresses that smell of BO, most definitely. In terms of ironing afterwards, you can buy an ironing cloth which is like mesh, you can then iron on the right side of the fabric but it protects the clothes from steam and prevents them from going shiny. (type "ironing cloths prevent scorch" in Ebay for an example.) These cloths are also fantastic on things like black cotton shirts, which often show up iron marks around collars and cuffs.
I am quite brave and wash most dry clean items in the washing machine excepting silk, which I handwash, and raw silk, which is the only item I would dry clean as it just can't cope with water.
Remove excess water by rolling item in a towel and standing on it.
To be honest you have nothing to lose from washing in the machine if they already smell of BO, as they won't be pleasant to wear.
And definitely get better deodorant. I use a roll-on and an invisible spray on top as well, in summer. I also put talc on all around and change bras every day as if your underarms are sweaty, your bra will be sweaty too 