There are various works in the recent literature on fundamental research and experimentation on unmanned aerial vehicle (UAV) communications. On the other hand, to our best knowledge, there is no taxonomy and survey on experimentation possibilities with a software-defined aerial wireless platform. The goal of this paper is first to have a brief overview of large-scale advanced wireless experimentation platforms broadly available to the wireless research community, including also the Aerial Experimentation and Research Platform for Advanced Wireless (AERPAW). We then provide a detailed taxonomy and a comprehensive survey of experimentation possibilities that can be carried out in a platform such as AERPAW. In particular, we conceptualize and present eleven different classes of advanced and aerial wireless experiments, provide several example experiments for each class, and discuss some of the existing related works in the literature. The paper will help to develop a better understanding of the equipment and software resources that can be available for experimentation in mid-scale wireless platforms, as well as the capabilities and limitations of such platforms.