your D5100 doesn't have an in camera focus motor. Thus it can only autofocus with lenses that have a focus motor built into the lens. From Nikon, these will be called 'AF-S'. Tamron will simply say 'built in motor', Sigma will call them HSM, Tokina will say 'AF-S motor'.
If it doesn't say one of those things, you will only be able to focus the lens manually, which for 'all arounder' zooms is annoying.
That's the biggest thing to note. It seems like all the lenses you've mentioned will focus with the D5100, though I'd want to triple check.
Next most important thing is VR, VC and OS. These all mean roughly the same thing. They lessen the visible effects of the camera not being held steady and make your pictures sharper if you take them at low shutter speeds. VR stands for vibration reduction, vc stands for vibration control, os stands for optical stabilization. ALL the same thing for all intents and purposes.
the next important thing is the mm range. The lower the number, the wider it goes, the higher the number the more zoomed in it is. So the bigger this range is, the more different types of 'zooms' it can do. generally, 18-30 are considered wide on a crop frame camera (which your D5100 is). These are good for landscapes, buildings, and anything you want to get very close to, but still have a bunch of in your frame. 30-50 are considered 'normal' lengths, and are good for day to day type pictures. 50-80 are considered mild telephoto and are good for portraits and other situations where you need a little zoom. 80+ are considered telephotos and are good for some portraits any anything you need to zoom in a lot for.
Next is the aperture. this is the f/x.x number. Aperture controls how much background blur you get (bokeh) and how much ight your camera lets in, and thus how fast you can make your shutter speed. the lower the number the better here. All of the lenses you mentioned are variable aperture, which means at the widest end of their focal range, you get the lower number, and the most zoomed in range you get the highest number as the minimum aperture.
If you want a 'do everything' lens, the tamron 18-270 is a do it all type lens. However, this means that it's not particularly sharp, and at the 270mm end (very zoomed in), your most open aperture is going to be f/6.3, which means you'll only be able to really use it in daylight, or on stable subjects on a tripod.
Most of the other numbers and letters can be more or less ignored for the time being, as they are super technical things about how the lens is made, that you don't really need to know unless you are very far along. And even then you probably still dont really need to know.