I am setting up a 70 amp sub panel in my detached garage, about 800 sq ft, from a 100 amp main panel, would a 2-3 copper wire be strong enough to support this? the run from main to sub is about 110 ft. I just plan on running 4 lights, 4 outlets and if I can maybe a 220v outlet for an air compressor....
First, on subpanel size, don't short yourself. A 70A panel is tiny. You may think "Oh, this satisfies my immediate needs, and que cera cera"... but really, panel spaces are cheap. Getting extra spaces now is a very cheap way to protect future plans. I wouldn't consider anything less than a 12-space (24-circuit) panel.
We see a lot of people spend stupidly unnecessary amounts of money on things like the wrong wire... and then turn around and chintz out on the panel. Overspend on the panel, it's one of the smallest expenses. See also...
The garage subpanel needs a main breaker
Well, to be more precise, it needs a disconnect switch at the garage. The cheapest/most efficient way to do that is a "main breaker" panel. I guarantee you a 70A panel doesn't have that, so rethink the panel choices to find one with a main breaker. Your alternative is an actual disconnect switch, but they can be $50 or more, and that plus your existing panel budget will get a really nice main-breaker panel.
1-1/4" conduit is a great idea
That gives you a lot of versatility. It also accommodates up to 125A of wire capacity.
You cannot use NM cable outdoors. Do not buy that.
Now, it really depends how much power you really want out there. From the loads you described, it seems like you could get by with a 30A feed. Remember you get 2 legs of that voltage, so I'm assuming a 15A 240V compressor that sits on both legs, and then two 15A 120V appliances on one leg each.
But let's be more generous and say 50A, because that's a happy number when using THHN wire in conduit. You can't do this with cable, but with THWN in conduit, you can use #8 copper or #6 aluminum wire (price it both ways). You need three THWN wires, and one ground wire (copper #10 will suffice for up to 60A).
You might as well use aluminum since the lugs are aluminum, and it's 1/4 the cost. Aluminum works fine in feeder like this.
If you really want 70A, then again THWN in conduit gives you an advantage as this only requires #6 copper or #4 aluminum conductors and a #8 ground. (cable would require a size bump).
If you go #3 copper or #1 aluminum you are good for 100A with a #8 ground.
(Above 100A you'll need #6Cu or #4Al ground wire).
The #2 copper you originally proposed (at $7/foot are you kidding me, $800 on wire??) is good for 125A. But you cannot use NM-B wire. If you really wanted 125A, then you should use #1/0 Aluminum for $200 lol. (with a #4 aluminum ground wire).
At 110 feet you do not need to enlarge the wire for "voltage drop". That's not a factor until about 180'.