Between recently, lately, and of late, there are minor differences.
"Recently" can mean one of two things:
- Simple past: An event happened recently. It happened in the recent past.
✓ I thought about my mother recently.
- Perfect: Something has been happening recently. It has repeatedly happened.
✓ I've been thinking about my mother recently.
"Lately" can only mean the second one. It's not natural to use "lately" for one particular event, generally described in the simple past.
I thought about my mother lately.
✓ I've been thinking about my mother lately.
"Of late" is the same as "lately". However, it's archaic. You might encounter it in literature, but I can't imagine a context where it would come up in conversation — except if someone is trying to sound archaic. :)
Between so far and by now, there are significant differences. But they aren't easy to articulate, because they both refer to the recent past.
So far means "up to the present time", with an emphasis on the future: something could change after this point.
There's no news about the get-together so far. But we might hear about it tomorrow.
You can replace "so far" with "yet" in the above sentence. In terms of syntax, you can't always fit "yet" in the same place "so far" fits, but the meaning is the same anyway.
By now means "before now", with an emphasis on the past: something should have already happened.
He left the house at 3? Then he must have gotten home by now.
You can replace "by now" with "before this point" in the above sentence. Again, this replacement doesn't always work in terms of the syntax, but the meaning is the same.
You can also use "by" with any given time. By Friday, by 4 p.m., by morning, by next year, etc.
I want you to hand in your work by Friday at 8 a.m. So anytime before Friday morning is good.
Here's a direct comparison of the two terms. You could not switch them around in these sentences:
So far, there's no news of your brother. We should have heard about him by now.
There may be news of him in the future. But there should have been news of him in the past.