Here is a picture of brand new rings form the Briggs & Stratton web site and as far as I can see they are identical to my old ones. The compression rings have a open gap of about 3/8", the upper and lower oil rings have a gap of about 2 mm and the curly ring in between has no gap, just like my old ones. But since I have it all apart I might as well install new ones to eliminate any doubt. I know I will have to hone the cylinders as well.

I am getting ready to order stuff. I need to know the following. Is sealant used on the valve cover gasket? Is sealant used on the head gaskets and is sealant used on the sump gasket? If yes, what type of sealant is
required.

Ok, 
 
Your not measuring the rings correctly..
 
They have to be put inside the cylinder, 3/4" -1 " down from the top...
 
Then you measure the end gap....  That's what'll show the wear on them...
 
Off the engine is useless..
 
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Thanks SRT for showing me the correct way to do it. I will get to it today. I looked at new rings vs my old ones for comparison purpose only to see if I detected something that was grossly out of the ordinary. What about sealant? Is any used on any of the gaskets?

You shouldn't need sealer anywhere..
 
I'd measure the old rings (and note it, then measure and note it...
Please post that back
 
Make sure you HONE the cylinders before re-assembly.  This helps the rings seat/seal.
Your manual or You Tube should show it..
 
Did you get instructions on where (in relation to each other) the ring ends go?
Compression and oil rings.  Compression "ends" usually 180 degrees apart from each other.
 
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Mine after honing and ready for re-assembly:
 
 

Post #16, the second picture of a ring,
 
Is that a compression ring and is it not completely flat on the edges?
It looks like some grooves/wear spots there, Maybe just the pic...
 
Advise..
 
 

On post #16 the compression rings are still on the piston. The ring you see is the upper oil ring IMG07, then followed by the funny looking wobbly ring IMG08 which goes in the center of the oil groove (what do you call that center oil ring - LOL?

Ok SRT, here are the measurements for the rings. The end gap of the compression rings is between .045 and .050". That's more or less on both pistons. The end gap of the oil rings is .026". The inner part (that wavy looking oil ring) barely touches the cylinder walls. That's pretty much the same for both pistons. According to my manual anything over .030" is bad. Oil rings seem to be good, compression rings bad, even though I measured a compression of 130. I am so confused. Why the unusual oil consumption?

I think you have a shop manual, so what are the spec's in there?
 
For instance:
https://hastingspistonrings.com/tech_tip/checking-compression-ring-gaps/ 
 
With that end gap, as you stated, at least the compression rings are worn, by quite a bit and definitly 
need replacing.
 
I think you already have new rings.  Put those in the cylinder and measure end gap (compression only).
It should be considerably tighter..
 
130 PSI is pretty good but the rings are definitly worn and oils getting past them.. 
 
With the new rings, you won't have nearly, (or vey, very little) blow by. 
 
With that said, you should hone the cylinders lightly to get some cross hatching so the rings seat
fully (for maximum life and sealing). 
 
There's really no way to measure the oil rings (to my knowledge) but if the compression ones are worn, the oil rings are likely worn as well...
 
With re-assembly, check your manual about where on the pistons, the ring end gap should be ON THE PISTONs, when they go back in the block...  Usually 180 degrees apart.  
 
Long  story short, I bought a Dodge slant 6 car (about a 1974) from a friend.  You could only drive about 10 miles and then ALL 5 QUARTS of oil was GONE...  And the engine ran great, no smoking either.  The engine bay was COVERED WITH OIL.   I cleaned the compartment to find the leak.  Oil was blowing out the DIP STICK HOLE, period.   Pulled the motor, heads pistons, etc.  Compression rings had 1/4" END GAP...  Cleaned, honed, put in new rings (one cylinder was just slightly out of spec-gap wise).  Re-assembled, no more oil loss/burning, etc.   BIL drove/kept the car for MANY years, no more issues...
 
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