As a nation, Oz doesn’t have much of a military force. It’s often stated that the Soldier with Green Whiskers is Ozma’s entire army, although we’re never told for sure what happened to the other officers and privates mentioned in Ozma of Oz, and presumably Captain Fyter counts as a soldier of hers on active duty.
Regardless, we’re definitely looking at a very small army, and one that we’re told looks good, but isn’t particularly skilled at fighting. Throughout most of the series, it seems that Ozma doesn’t need military might because of all the magic she has at her disposal. Even as early as Emerald City, the Ozites defeat a foreign invasion force led by the Nome King by tricking them into drinking the Water of Oblivion, then using the Magic Belt to send everyone back home. In Wishing Horse, Pinny Penny informs King Skamperoo of Skampavia that, despite the number and skill of Skampavian fighting men, they would be no match for Ozma’s magic. And in Ozoplaning, the Stratovanians temporarily succeed in taking over the palace, but are soon banished by the Wizard of Oz. For the most part, it’s technology, not physical force, that enables Ozma and her subjects to defend themselves.
This does leave open the question as to what would happen if something were to go wrong with this magic, but Ozma and her friends end up with so many different powerful items at their disposal that one of them is bound to work in just about any situation. There could still be some challenge involved there, and Ruth Plumly Thompson was especially fond of making villains temporarily triumphant due to taking advantage of lax security (a topic that I might well make the subject of an entire post at some point), but it usually makes Oz as a whole pretty much unbeatable.
There is, however, one major fighting force in Oz that I haven’t mentioned, and that’s Glinda’s all-female army.
It doesn’t show up all that often in the series, but when it does it’s described as quite formidable. This army plays a significant role in taking the Emerald City back from Jinjur and her Army of Revolt in Land, but we don’t actually see them fighting, essentially because they don’t need to. Once Jinjur and her followers, who are armed with mere knitting needles, see the “very grand and imposing” army outside the city, they barricade themselves inside and start to rely on Mombi’s tricks to keep the Munchkin girl on the throne.
Indeed, when L. Frank Baum describes the army, he comments more on their appearance than their skill, keeping with the general idea in the Oz books that the primary function of soldiers is to look important. That said, they are all armed with spears and swords, and presumably would be skilled fighters in a situation in which force is necessary. When you think about it, Glinda is a vassal ruler under Ozma, yet she has a much more powerful military than the ruler of the entire land does. She presumably keeps it intact in case a situation arises that can’t be solved with negotiation, trickery, or magic (and Glinda is quite skilled in those areas as well). I think it’s a good example of how, even if it doesn’t come up in that many books, Glinda is the true power in Oz. She put Ozma on the throne, and if the fairy princess were to ever prove troublesome, she probably feels she could take her OFF the throne. Not that the sorceress likely has any such intentions, as she and Ozma are on the same side, but I have to suspect that the Quadling ruler has developed contingency plans for situations that the often ill-prepared Ozma hasn’t even considered.