competitive equilibrium, Walrasian equilibrium, Walrasian auction There are several sellers holding some indivisible goods, and several potential buyers with different valuations for these goods.  I need to calculate the Walrasian equilibrium in this scenario, but first I need to understand what exactly is a Walrasian equilibrium. So I am looking for a short, formal, operational definition of this term.

Wikipedia just links to a page about General equilibrium theory, which is very long and verbal, but I couldn't find there a formal definition of a Walrasian equilibrium.

This page also hints that a Walrasian equilibrium is similar to Competitive equilibrium, but I didn't understand whether they are identical or different, and if they are different - what is the relation between them?

There is also a page about a Walrasian auction, but again, I am not sure what is the relation between this and a Walrasian equilibrium?

The definition in the about.com dictionary looks promising: "An allocation vector pair (x,p), where x are the quantities held of each good by each agent, and p is a vector of prices for each good, is a Walrasian equilibrium if (a) it is feasible, and (b) each agent is choosing optimally, given that agent's budget. In a Walrasian equilibrium, if an agent prefers another combination of goods, the agent can't afford it."   But, they do not define what they mean by "feasible".

I would very much appreciate an orderly explanation of the relation between all these different terms.
The definition from about.com is what you are looking for. Feasible means that total consumption of each good does not exceed total endowment (initial holding) of that good in the economy. Terms Walrasian and Competitive equilibrium can be used interchangeably here and Walrasian auction is entirely different concept.