Norwegian, spoken by only 5 million population, is under-representative within the most impressive breakthroughs in NLP tasks. To the best of our knowledge, there has not yet been a comprehensive evaluation of the existing language models (LMs) on Norwegian generation tasks during the article writing process. To fill this gap, we 1) compiled the existing Norwegian dataset and pre-trained 4 Norwegian Open Language Models varied from parameter scales and architectures, collectively called NorGLM; 2) introduced a comprehensive benchmark, NLEBench, for evaluating natural language generation capabilities in Norwegian, encompassing translation and human annotation. Based on the investigation, we find that: 1) the mainstream, English-dominated LM GPT-3.5 has limited capability in understanding the Norwegian context; 2) the increase in model parameter scales demonstrates limited impact on the performance of downstream tasks when the pre-training dataset is constrained in size; 3) smaller models also demonstrate the reasoning capability through Chain-of-Thought; 4) a multi-task dataset that includes synergy tasks can be used to verify the generalizability of LLMs on natural language understanding and, meanwhile, test the interconnectedness of these NLP tasks. We share our resources and code for reproducibility under a CC BY-NC 4.0 license.