Not even Janitors can directly delete nodes. The founding forefathers deemed this to be a particularly worrysome power, to be used sparingly.
If you have authored a node that you wish to have deleted, consider the node for deletion using the moderation nodelet. Give a compelling reason, because folks will have to vote on it. And it will need to accumulate a slightly negative XP.
It is problematic to delete nodes that have replies. Since it's impossible to know if someone is in the middle of typing a reply to a node that is about to be deleted, there exists the potential for race conditions that could leave replies floating without parents, and thus without context.