I've seen and heard and used the acronyms ASAP ("as soon as possible") and PDQ ("pretty damn quick"; in fact, my favorite childhood chocolate-milk mix was PDQ granules -- which did dissolve instantly).
And I've heard another phrase that means "right away," but hadn't used it myself -- (whew) -- or even seen it written until a few weeks ago, when an editor copied me on an email in which she asked that something be sent to me "tout de suite."
Ack! -- I hadn't known the phrase was French, and was intensely ashamed at whatever ignorance had led me to imagine it as "toot sweet." But I felt a little better after some research, where I learned that English-speaking soldiers had anglicized it to exactly that during WWI.
I emailed the editor and thanked her for the best thing I'd learned that week. She responded that it was nothing -- it was the writers whose emails and manuscripts included "wa-la!" (um, "voila") that surprised her.