What is the correct meaning of dhamma, dharma, atta, anatta?

The word 'dharma' means 'that which supports'. The following things support life & spiritual life:

1. natural things or phenomena, such as food, oxygen, trees, people, mind, Nibbana, etc

2. knowledge of natural law or truth

3. practise or duty or spiritual paths

4. results of pactise or duty

All of the above are meanings of the word 'dharma' dependent on context.

The phrase "sabbe dhammā anattā" means "all things/phenomena are not-self", which includes Nibbana.

As for the word "atta", it means "self" rather than "soul". If "atta" meant "soul" then the Buddha would not have been required to teach "the body is anatta" (given most people distinguished between the body & the soul). "Atta" refers to the sense of possessiveness, which ultimately creates suffering, namely, "I", "me" & "mine".

In one of our conversation, you wrote that you are from nepal... So here I will use some hindi language too. Don't confuse from various representations of dharma, dhamma, atta.

Dharma( धर्म ):: This word was already there in India even before buddha. Even Aghoris used to use this word. This also includes the wrong views of attaining liberation and/or gaining merits through sacrificing ( बलीप्रथा ) animals and humans( नरबली)--even nowdays these are being practiced.

Dharma was/is referred to all the principles that govern this universe.See Hinduism part Such sets of principles were/are considered to be right view. Eg., dharma of a kshatriya is only to fight&rule, dharma of various castes, dharma of fire is to produce heat, and so on, dharma of deva/ghost/... is to eat material food, and so on...
Note as to how dharma is generalized to meanings of behaviour, duty, karma, requirement_for_satisfaction of celestials,... Now, buddha arrived::

After attaining enlightenment, having Right view, he sees that dharma of human has nothing to do with caste, satisfaction_dharma of celestial beings has nothing to do with materials,...
So, a new term has been given, simply because it would be too much troublesome to waste time on teaching right_dharma without an appropriate word.

Dhamma:: Set of all the right principles governing universe, so simple.
These principles are also concrete cause they are being told through Right View in righteous way(8 fold Noble path).

Atta:: This is a generalized word for 'self'. It can be used to mean inner-self and outer-self. Atta, when used to indicate seemingly 'I' means 'inner-self', when used for other things means 'outer self', i.e. self of other things.

Sabbe dhamma anatta:: It means that all the right governing principles are not-self(this self is outer-self), means that they don't have any permanence within them.

This statement was specifically given for those people who declared buddha to be God( परमात्मा/parmaatma/eternal-self ) and hence principles given by him as his child( आत्मा ) buddha as vishnu...to remove wrong view among people.
Along with this, dhamma states it's permanence in sense that from infinite past-time, these principles are true&right, at present these are true&right and in infinite future time these will be true&right. Buddha also states it's permanence as,"Whatever principles have been given were, are and will remain true&right".

So, to avoid any misunderstanding, he simply said, " I have no atta, dhamma also has no atta".

That's it. No confusion.
Metta.

The word dhamma in these passages has multiple meanings and can only be understood in the context of the passage they come from as you seem to understand. This is difficult for most Buddhist students and anyone who does not speak the original language of these ancient texts. That is why it is important to rely upon good translations and on good spiritual mentors to explain and expand upon the context.

Of course, it is wonderful that you are trying to piece together the meanings and different contexts of how the word dhamma is used in these passages! But even more important is to try and figure out the underlying teaching without fixating on individual words.

I would encourage you to see if you can't paraphrase each passage yourself in plain english or whatever your native language is and try no to worry too much about what the word 'dhamma' really means as it is not (like all words!) a real and substantially inherent thing. What it means is entirely dependent upon the context it is used. What's important in all these teachings is the heart or spirit of the teaching and not any individual words and to get at them we must consider the context.

I think that "atta" and "atman" are the same words, two different languages (Pali and Sanskrit).

That in a Buddhist context, "atta" (and its converse, "anatta") are related to ideas like upādānakkhandha (from SN 56.11) and sakkāyadiṭṭhi ... and furthermore that (according to doctrine) any/all theories about self (or "self-existence"?) are unsatisfactory or cause suffering.

And that "dhamma", there, should be understood there as in contrast to "sankhara" -- i.e. that, "all sankharas (all constructed/compounded things) are impermanent and unsatisfactory", conversely, "literally everything (including for example nibbana) is anatta (although nibbana, which is a dhamma and not a sankhara, is neither impermanent nor unsatisfactory)".

There are two languages, Pali and Sanskrit. Pali sounds like a mumbled version of Sanskrit, basically. Many of the consonants found in Sanskrit words are skipped in corresponding Pali words.

So Dharma is Sanskrit and Dhamma is Pali. Atma is Sanskrit and Atta is Pali. Anatma is Sanskrit and Anatta is Pali. Sarva is Sanskrit and Sabba is Pali. Nirvana is Sanskrit and Nibbana is Pali. And so forth.

As for the meaning,

Dharma/dhamma comes from the root "to hold" - so it means "that which is (up)held" - either an Order of things at large (a system, a tradition, a law, a teaching, a way of living) or an individual element of such order - "a thing", "a phenomenon", "a happening".

Atma/atta is something like "core" or "kernel". For living beings it is their innermost "spirit" aka "agent" and "subject" - that presumed homunculus inside of us which watches through eyes, listens through ears, thinks thoughts, and makes the impulse to act. For inanimate objects it is their unalienable identity, that which makes them what they are.

Anatma/anatta is simply a negated form of the above. It means ontological absence of any such innermost agent, subject, unalienable identity.

Based on all of the above, the Pali phrase

Sabbe dhammā anattā.

Would mean All (Sabbe) Things or Phenomena (Dhamma) are Without A Fixed Core (Anatta).

In other words, the living beings do not have any central core where all experiences come together and all action is initiated. And the inanimate phenomena do not have key pieces that would alone define their identities. For example water does not have one key ingredient that makes it water, it is a particular combination of elements working together is what gives it its specific qualities.

from an EBT (early buddhist text) perspective: http://lucid24.org/tped/d/dhamma/index.html#dhammamsutva

☸Dhamma, dhamma

1. ☸Dhamma = The Buddha's Teaching.

2. Dhamma = Natural laws of the universe, like impermanence, death, illness, etc.

3. dhamma = idea/thought cognizable by the mind (6aya): 💭 manasā dhammaṃ viññāya.

4. dhamma = thing. A broad term that can mean anything.