What word should I use in informal speech for connecting cause and effect just like から does in polite form?
Use から. It's not only used in "polite" speech (it doesn't actually matter what you mean by that), but also in "informal" speech.
If から reminds you too much of K/J-Pop, you can sometimes replace this から by ので/んで e.g.
but you'll likely end up sounding more polite than when using から.