Looking at the problems what you are facing it seems your engine is lacking compression.That means there is a leakage of pressure created by the combustion of fuel.This can be due to:
1) Leakage at the valves- It can be due to a burnt valve or a bent valve stem or improper seating of the valve on the valve seat due to natural wear and tear. If this is the case its the least costly engine repair. Dont reuse the valves again by grinding. Go for a new valve seat and let the mechanic make the new valve seat proper on the valve seat. Might be valve guides will also be replaced.For this the mechanic only remove the cylinder head.
2) Leakage between the piston and the cylinder block: This can be due to worn out piston rings, which is also a less expensive repair. The mechanic just needs to open the block and change the piston rings to new one.
It can be also due to worn out piston/seized piston/Cylinder block wear and becoming oval/scratches on the cylinder block liner walls etc and is the most expensive repair. If this is the case go for a completely new block of engine and piston and also replace the valves or do valve seating to ensure you need not remove the engine again and again.
Once you open the entire engine block you might land up with more cost like replacing Big End/Small End Connecting rod bearings/Gudgeon Pin/If required a replacement of the defective Crankshaft. Oil seals etc.It is better to replace big and small end bearings if you open the engine completely.
Not all honda engines last long,and if you have done anything above 50k-60k kms then you might be needed to do all the above things.
What you need to do:
1) Search for local mechanics in your vicinity who are experts at doing specially engine overhauling work. This is the most difficult task. It doesnot matter whether a Honda Service centre mechanic or a local mechanic does it. Both can screw your engine, the difference only would be that the Honda service centre would charge you minimum double the cost of a local mechanic. The person who carries out your work is the most important criteria here.Before you give the vehicle to the mechanic its better to get it washed thoroughly from inside to maintain clean environment.
2) Once you find the local mechanic, tell him that you will get all the major spare parts for the work to be done and get a list of spare parts to be purchased.Fix the labour cost with the mechanic and ask him what is the problem. Try to seggreate the problem as per point one or two and think of the expense incurred accordingly.Go to Honda showroom or a good automobile parts dealer and get all the original spares. Be specific while asking for original only. Ask for discount if buying at local shop!!
3) For small parts let the mechanic buy it for you.If the mechanic is good he will pay good attention to the cleanliness of the parts etc. Dont let him keep the parts on floor where dust particles can get inside.Use a newspaper instead to keep the same.Also carry clean waste cloths for the mechanic to use.
4) Take a day-off and stand nearby to him while carrying out the work entire day if possible. Take a lot of pics for us
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5) Use fresh engine oil and a fresh new oil filter.
6) After the work is done make sure to do average calculations and keep it as note for coming months to see the average figures grow. If the first day itself the engine is giving very very poor average then that means that the work was not done properly. The engine should run tight like a new engine but not rough.
7) Do a proper run-in procedure.
What not to do:
1) In any cost dont go for rebore or oversized pistons.Very few people in india have the capability to carry out these jobs and even if they have they dont have the right machines which are capable to achieve the tolerances as required.
2) Avoid duplicate parts.