As far as I can tell, there is a certain way that God reveal's Himself to people where this is essentially no doubt it is God ... whether He is speaking, or doing something specific, etc. You may not have the right word for Him, but He is who He is, and in my experience, ANYONE can recognize Him in that manner. Doesn't matter which religion you are, what your personal belief system is, atheist, Zeus worshipper, whatever. It is as though there is an instinctual response to the Creator, as though He truly is the Alpha, and somehow we know this and it is revealed. In the specific ways you mentioned above, yes I believe God still speaks to people in those manners because I can think of modern examples and personal accounts.
Likewise, the Holy Spirit can move upon people in such a way that it is undeniable that SOMETHING is effecting them. Again, I've seen all walks of life respond to the Holy Spirit, regardless of their level of belief or lack of it, even atheists. Similarly, they may have not had the words for the Holy Spirit, but they acknowledged something powerful and spiritual was present and effecting them, the situations, etc.
Other spirits can reveal themselves (which I don't believe are God) in certain ways and it can be discerned by people who are used to interacting with spirits and discerning them. Sometimes these spirits will even identify themselves. Again, regardless of your walk of life, in my experience pretty much anyone is able to at least acknowledge these spirits. Discerning more details about them may differ from person to person however. Also, typically the atheist does not acknowledge these spirits in my experience, and I may argue that most of them are unable to, and thus I can see why most claim there is no such thing as supernatural beings. I believe these types of spirits often confuse most believers who recognize they are spirits and different from the "norm", but can't decide whether these spirits are God, the Holy Spirit, angels, etc or not lol. There may be multiple reasons for this confusion amongst those who believe. When meeting, or interacting with spiritual beings who are different from us, it can be easy to see why a person may confuse such a being with being either a "god", or God Himself without many points of reference.
I believe the most confusing "Being" for people to identify is Jesus and other children of God, actually. From the scriptures this rings true, and in my experience it still rings true today. I believe that the Lord can be in a situation and you not even realize it. Same as His brethren ... it may not always be obvious whom the Children of the Kingdom are to everyone. I also think there are multiple reasons why this is so, as I can think of a variety of scriptural instances where there was confusion even amongst those whom walked with Him Jesus before and immediately after His crucifixion.
