are they bugged? They give minus to strength even when having slow poison and death ward active....

Mandragora swarms drain blood. That's what is doing str damage. Their poison causes confusion.

Any protective spells that makes you immune to them or just have to kill them from afar?

The latter. Technically, if you had no blood to drain you would be immune to them, but you can't become a lich or some such in this game. Even Jaethal does have blood still, although I don't remember if she gets drained or not.

It's not bugged, death ward doesnt provide immunity to attribute damage.
Fiery body is the spell that protects from attribute damage (among other effects). You can tank those most with a character possessing it (properly built sorcerer, cleric or druid).

Lucky accident when I first came across these, but it helps to have a "meat shield" of skeletons ahead of you. You may still get hit, but it shouldn't be as severe as if you went all-in on them yourself without summons.

Blood drain also shouldn't work if they can't overcome your DR, yet I think it still does.

edit: I can also confirm that they have fast healing even in the dead of night.