So, I've built a multinomial logit model (with 4 classes) that has log loss equal 0.945. My benchmark model (probabilities equal classes distribution in train sample) gives log loss 1.131. How can I understand if it is good/ok/bad model by comparing these values?
There is no general answer to such a question. It depends on things like what the variables are actually about and what other models you're considering. In any case, log loss is unlikely to have an immediate intuitive interpretation. It is more useful as a model-selection method than as a way to understand the model's accuracy in real-world terms.