Because
Saya tidak datang karena hujan. ‘I didn’t come because it was raining.’
Answering a kenapa question, you can start with it:
Kenapa telat? ‘Why are you late?’
Karena macet. ‘Because of the traffic.’
So
Jadi introduces the consequence.
Hujan, jadi saya di rumah. ‘It was raining, so I stayed home.’
Jadi also opens a summary, exactly like the English “so”:
Jadi, bagaimana? ‘So, how about it?’
And it has two unrelated meanings you will meet: ‘to become’ (jadi guru, ‘to become a teacher’) and ‘done, on’ (Jadi nggak? ‘Are we still on?’). Four jobs for one word, and context carries all of them.
Soalnya, the one people actually say
Soalnya is the casual ‘because’, and it is far more common in speech than karena.
Aku nggak bisa, soalnya ada kerjaan. ‘I can’t, I’ve got work on.’
It can also come first, meaning something like ‘the thing is’.
Soalnya begini… ‘The thing is…’
Makanya
Makanya means ‘that’s why’, and it carries a small edge of I-told-you-so.
Makanya, jangan lupa. ‘That’s why I said don’t forget.’
Used between friends and from parents to children. Said to a stranger it would be rude.
Two orders, same meaning
Indonesian is relaxed about which half comes first.
Saya di rumah karena hujan.
Karena hujan, saya di rumah.
Both are correct. The second puts weight on the reason.
What you’ll actually hear
What the book says: Saya tidak dapat hadir karena ada urusan penting.
What you’ll hear: Nggak bisa dateng, soalnya ada urusan.