i am wanting to lock my rear diff whats the easiest and cheapest way

It may not be the easiest but the hands down cheapest is welding. 

It depends on how you use your Zuk.  Is it a daily driver, off-road, or both?

Three cheapest/easiest ways to lock a rear diff:
1. Welding
2. Spool or mini-spool
3. Lock-rite locker

My opinion:
Cheapest = welded spider gears
Best = mini-spool

Easiest: With the exception of the welding process, there is no difference in install of welded gears or a mini-spool. A locker is a little more involved but not very much.

i just use it for off road use only

I would use a spool, I run a lockrite in mine and have for about 7 years and have not broken a rear one yet (4 fronts) if it ever does break I will put a spool in there. if you weld make sure you get it welded well, if it breaks it will probably take your ring and pinion with it.

What about the strength of the stock axles do they hold up well with a rear locker

The 3 ways to lock a samurai axle.......

spool, welded, lock right.

Best ways in order (IMO).....lock right, spool, weld.

Lock right.....harder to set up, but best overall for being easy on the axleshafts (not as much binding as with the other two).  Some guys have issues with lock rights not operating correcty, but I think that is usually either because of improper setup, wear, or bent axle housings.

Spool.....really easy to set up/install, but the axle shafts are locked together permanently, so there is no give (unless the tires slip) when making turns.

Weld....you need to know how to weld (and how to weld correctly), for this to work.  As mentioned, if the weld breaks, then it will probably damage other things in the diff.  Highest potential for failure, IMO.  Same characteristics as a spool.

I have an off-road only samurai and considered all 3 when I was adding a locker to the front.  Meaning, I was going to take the lock right out of the rear and move to the front, then relock the rear with either a spool or weld, or I would just just add a new lock right to the front.
After considering the pros and cons of each, I ended up just leaving the rear lock right in place and adding a new one to the front axle.
I had no axle issues running front and rear lock rights with 31" tires.  I have started running 33s and have had no axle issues with them either...but I have only ran them on 1 run, so far.  The general consensus is that stock axles will hold up to 31s without much problem, 33s are pushing it.....of course this all depends on your driving style and terrain you run.

I agree completely with Kevin.  I've got lock-rights front and rear, and I love them!  The thought of dragging my tires around corners never appealed to me.

Let's say that we're on a trail with no straight roads where the average radius of the curves is 300 feet to the center of our road.  My Sammi has a track of about 55 inches.  My outside wheel will make a curve that has a radius 55 inches greater than the radius made by the inside wheel. For every mile that you go with a welded dif or a spool, you're dragging your tires over 81 feet.   Sounds like a bad idea to me.  Tires are damn expensive!  I'd rather put the money I save from tire wear into lockers.

It's easier to drag tires in the dirt/gravel than on asphalt, but what about a rock face or a shelf-road?  I consider the lockers to be cheap insurance.

Driving with a locker in the front and no power steering makes for upper body exercise.  I expect that a welded/spool in the front without power steering would be downright dangerious.

(300*12)=road radius inches 3600
Track is 55 inches
outside wheel radius 3600+(55/2)=3627.5
inside wheel radius 3600-(55/2)=3572.5
The percent of change is 1.53953813 %
(1.0153953813 * 5280)-5280=81.287613264 ft.

It really depends on your tire size and driving style - the stock rear axles are pretty tough (compared to the front)

Go spool in the rear IMO