Last year I changed old chain, all cables, rear and front derailleurs with new cheapest shimano parts. It has 7 speed cassette with tourney 6/7 speed rear derailleur. As summer started I took this bike for a ride and then immediatelly noticed this strange thing. When I pedal harder there is a loud noise which looks like is coming from rear wheel (feels like chain would slip) end and then it seems like the chain would slip and my feet goes all way in and there is just loss of force. Basically the bike is unusable whenever you try to pedal any harder. I tried to see if there is actual slippage of chain but it doesn't look like that is happening. Then I tried to inspect if freehub is somehow skipping as I read somewhere that this could be the problem, but it engages correctly and doesn't slip. The cassette is quite old but it's teeth still look ok. I tried to change chain, all cables and even tried different casette. But the problem persists. I tried to readjust both derailleurs. When I try test this without actually sitting on bike and pedalling this never happens. Gears are shifting smoothly. However, when I sit on the bike and try to pedal. Immediatelly this chain slipping sound happens and pedalling becomes useless.
Slipping freehub pawl mechanism would be the prime suspect.
The reason it slips when you are riding is the increased force you are putting through the drivetrain.
There are number of questions and answers on this site about slipping freehubs. Sometimes dried grease is merely preventing the pawls from engaging properly. Next step would be to conform the freehub is the problem - have a friend watch you ride, they should be able to see if the chain is riding over the cassette sprockets; then investigate how to remove the freehub body from your hub.
If the skipping started happening right after you replaced the chain, I would suspect that the cassette needs to be replaced. If the chain has excessive wear, it causes a wear pattern on the cassette that will prevent the new chain from engaging properly under heavy pedaling load. It is hard to discern this wear pattern by visual inspection.
This situation can be avoided by replacing the chain before it's worn excessively. When the chain wears, the wear is on the pins, so the chain gets longer. The chain should be replaced before the increase in length is 1%.
Wear can be checked by measuring the length over a number of links using an accurate scale. The pitch (distance between the centers of pins) is 1/2 inch, so a new chain should measure 12 inches over 24 links. The chain should be replaced before this measurement reaches 12 + 1/8 inches.
Alternatively, there are special chain wear measurement tools made for this purpose.