The idea of non-self is straightforward. It combines the ideas of 'I am Nothing' and 'Everything in the Universe is changing'. Basically, if I attempt to say 'I am X' where X is some tangible phenomena (some sense object or the body or some mental phenomena), that attempt fails to produce a meaningful statement. Why? Because every X that we try to substitute in the statement 'I am X' fails except for X = 'consciousness' (the one who witnesses / perceives / experiences). The right statement is 'I perceive X', for example, 'I witness a tree', 'I perceive a sensation in my foot' or 'I experience anger'. Another way to say these is 'A tree has arisen in my consciousness', 'A foot sensation has arisen in my experience', 'Anger has arisen'. Additionally, since everything in our experience / consciousness keeps changing, it is futile to associate 'I' with any individual impermanent phenomena.
The idea of emptiness is basically the same as non-duality. If it is understood that everything in The Universe is basically happening inside you, that it does not have its own independent existence, then it's the same as saying that 'The Universe' is empty, there is nothing 'intrinsic' in it.
Emptiness is explained in the Heart Sutra. See Translation of Heart Sutra by Thich Nhat Hanh. Emptiness is basically the same as impermanence and non-duality put together. The Diamond Sutra is another fascinating Buddhist sutra that is difficult to decipher. I believe the Diamond Sutra is another exposition of Emptiness (change and non-duality put together).
Below is a Buddhist story that exemplifies the concepts of 'no ego', 'no I', 'non-self', 'acceptance' and 'I am nothing' :)
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