The answer to your question is no, there is no element with no liquid state. The state of an element (or molecule) depends on the temperature and the pressure. All elements can be in any of the three states (solid, liquid or gas) with the right temperature and pressure. We say that oxygen is a gas because at standard temperature and pressure it is in gas state, but if the temperature is low enough it will condense into a liquid and if temperature is even lower it will become a solid bulk. The opposite happens when increasing temperature but of course from solid to gas.
There is a phenomenon known as sublimation, this is when a substance (carbon dioxide for example) goes directly from solid to gas, leaving no trace behind. This doesn’t mean that you cannot obtain it as a liquid, it means that at our normal pressure and temperature it will pass directly to gas, but if the conditions are different then you could have it as a liquid. I know only two elements (pure elements) that can sublimate: iodine and arsenic. But again it does not mean that they don’t have liquid state