Socialism is not intrinsically linked to a strong state, or indeed any state at all. An oxymoron is a contradiction in terms. Anarcho-monarchy would be a contradiction, as a monarchy is a form of government itself.
Socialism is not a form of government - it is simply the advocation of certain economic ideas: equality of outcome, collective ownership, etc. Within socialism, there are disagreements regarding how you achieve these outcomes (and the degree to which those outcomes should be pursued). Certain strands of socialism might exclude the prospect of anarchism, but other strands of socialism are dependent on anarchism for their very foundations.
You introduce a premise: "without government intervention economic equality could not be achieved or maintained". The rejection of this premise is foundational to anarcho-socialism. State socialists believe you need to use the power of the state to maintain a system of socialism. Anarcho-socialists believe the opposite. They believe that for the conditions of socialism to exist and thrive, you need to dismantle the state. They see the state as another power structure that promotes inequality by placing some individuals in positions of power above others. You'll find anarcho-socialists advocating for communes and self regulating systems of cooperation, rather than socialism forced upon citizens by the state.
You might say that a situation where you have equality and no state is unrealistic. If true, that wouldn't make anarcho-socialism an oxymoron, it would just make it a flawed political philosophy with limited practical applications. I don't wish to provide a list of arguments for and against the merits of self governed communes and similar anarcho-socialist ideas, as it seems to be beyond the scope of your question.
Noting your last point, where you question how you could have the "duty to give away excess wealth" at the same time as "freedom from coercion", I think you'll find it interesting to look up some anarcho-communist conceptions of human nature. Broadly speaking, anarcho-communists believe in a fundamentally cooperative human nature, which would mean that people wouldn't need to be coerced into helping others, but would help others out of a desire to maintain human relationships and to mutually benefit from shared knowledge and resources. They believe that the state and capitalism have distorted this human nature (making humans selfish and interested in producing profit) and that dismantling those systems would see a return to their more caring, cooperative natural human nature. Kropotkin's work 'Mutual Aid' is a key text in this area.
I've provided some links that might be a useful starting point in researching anarcho-socialist conceptions of human nature further:
Wikipedia: Anarcho-communism: Motivation
Stanford Encyclopedia of Philosophy: Anarchism
Wikipedia: Marx's Theory of Human Nature
Scientific American: an article about Kropotkin