So 70D & 11-16 F2.8 basically. I would think the slower kit glass you have would not be ideal, since most clubs are crowded, and the point of the club is the ambiance and environment, so going ultrawide is a good way to capture it. Also, F2.8 is your friend. So I would stick with the 70D + 11-16 F2.8 for this. It lets you get very close to groups and get everyone, it lets you get tons of depth of field regardless of aperture, so you can generally just shoot at F2.8 and not even worry about people not being within depth of field after you focus (unless you're within a few inches of them, hah!). The F2.8 speed lets you shoot at whatever ISO it takes to get the shutter you want to stop motion--if you want that, some like the blur. If you want to get creative with blur, use one of your image stabilized lenses and just open the shutter up, I'd use the shorter, smaller lens (18-55) to reduce weight and make it more stable to hold steady for that longer duration, if you were into that. Getting a fast shutter is going to take a lot of ISO (don't be afraid of going to ISO 12,800!), if you want to stop hair and hands from looking like blur. For people standing around, not dancing or moving fast, you can generally get fast images at slower shutter speeds, but I wouldn't go too slow, as you don't want to miss the shot and find out later when you review them--you can't repeat that shot after all. I'd go for 1/60s~1/100s as a ballpark. For dancing you need much, much faster--faster than you'll be able to do without being severely under-exposed. This is of course depending on the club's lighting, most are quite dark though.
Things to consider:
Meter - Your in camera meter will be fooled, constantly, depending on what meter mode you use. Clubs are dark spaces with bright bits of light in different spots. If you use evaluative metering, your camera will see those bright lights here and there, and meter to that, and basically ultra-under-expose your subjects (people; assuming?) because of it--if you're using an auto or semi-auto exposure mode. If you tighten the area that the meter looks at, you can make sure you expose more of what you want, and less so what's in the corners and all. Partial or center can be useful for this. That said, you don't want to key-expose a subject and blow out the environment. So you'll have to find a balance between the lights an the subjects which means under-exposing some, over-exposing others, etc. Ideally I would just shoot manual, meter, take an exposure, look at the histogram, and push it to the right.
Exposing - If you're not already comfortable with ISO 6400 & ISO 12,800, now is the time. You will want to become very comfortable exposing at these values, which means, you have to be careful how you expose. Exposing a little to the right will help these files come out clean, in RAW. If you're shooting small JPG, then, well, you may not want to do this for a magazine. But if you have a minute to process, RAW and high ISO with some exposing to the right on the histogram will produce plenty clean files, and you can easily clean them up (Topaz denoise is great, I shoot at ISO 12,800 without fear as long as I expose correctly or slightly to the right).
You don't like the look of poorly controlled flash, I would be willing to bet. Flash can be a powerful tool, when it's not pointed right at your subjects and looks like cold, white light, with spectral highlights on sweaty faces, with the warmer, darker ambient light behind them. That's awful. I agree. But, blended flash that is bounced or indirect, so that it acts as fill instead of key with a gel to match it to the right temperature of the club, makes images pop! Suddenly you can see details in eyes, little catch lights, a little dazzle on the clothing, texture shows up. A well controlled ETTL bounce can do this. Not all clubs like flash though. But don't discount well controlled lighting just because you've seen poorly controlled, bad flash photos. Really good lighting control can produce amazing photos that you thought were ambient, but were really flash.
If you were to consider a new lens, I'd look at a 35mm F2 IS or 24mm F2.8 IS (for the stabilization at F2 and F2.8 for the really, really dark clubs). I would take 4 stops of IS over F1.4 in a club. The reason? Depth of field! F1.4 in a dark space is very easy to miss focus, it will be off all the time with a camera that cannot pierce the darkness and focus fast and accurate at -3EV or more (and the 70D cannot!). F2 and F2.8 or even F4 gives you a lot more chance of getting them in focus even if focus doesn't land perfectly simply due to depth of field. Also, again, seeing the environment in a club is part of the club after all. So if you stop down a bit, you want image stabilization. Also, wider aperture means better AF performance (F2.8). Using a slower F5.6 lens (ie, maximum F5.6 aperture, not that you have this, I think yours are F3.5 or so at their widest on your kits) for example, will not have the same accuracy of AF in the dark as the F2.8 lens does. Another lens to look a watch on would be the Sigma 18-35 F1.8, it's fast, has great focal lengths for tight spaces, and very sharp. It's heavy though, and big. Overall, wider angles are more forgiving of both shutter speed and space constraints which are big challenges in clubs.
Distance to subject is where distortion comes in, not the focal length (focal length is a factor in how field of view is determined; and that field of view helps you figure out your distance to subject for composition). If you get really close to people, they will get distorted. Sometimes you embrace the distortion (fisheye). Sometimes you avoid it (making girls' noses look big, or weird legs in corners, etc). Ultrawide is great if you're doing groups at a bit of a distance (3~4 feet), but if you're doing lots of frame filling face shots of two or three people, you might want something a little longer, like 24mm~35mm. I wouldn't go much longer than 35mm on APS-C in a club personally unless the venue was like an outdoor concert.
If you ever get a wild hair to get a more dedicated setup to this kind of shooting, look into a Sony A7S II and a fast wide angle lens around 17~24mm ranges. You can shoot in the dark with that thing.
Personally, I would just use an ETTL bounce with a head diffuser, with some -FEV dialed in to have it act as fill light (ie, it just fills in shadows, doesn't act as key exposure), and I'd velcro tape a gel on it to match the temperature of the club (either CTO 1/2 or so if it's one of those tungsten lit venues; in a cold temp venue, you can get away without a gel pretty often). And the flash would be on a battery pack to speed of recycle time. I would shoot at very high ISO (3200, 6400, 12,800) to force the flash power down, and make the duration of flash extremely short, and reduce the power needs so that you can basically shoot all night on that one battery pack. Camera settings would be to ambient light, and I'd use that ultrawide with an aperture around F2.8 & F4. That's if the venue allowed flash and the ceilings were not gymnasium level height, this is assuming flash is allowed, and the ceiling is more like a ball room or warehouse.
Flash & IS tips:
With flash, you can open the shutter really long, and move and blur the environment and lights, and flash will freeze an exposure of your subject even if they're moving. That's how you get those looks.
Image stabilization will let you keep something/someone static well focused and not blurred, while others move, and produce blur, if your shutter is slow enough. That's how you get that look with ambient light.