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Pushing a wall exhausts us. Why do we get tired, even if we arent doing any work ?

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Hmm interesting point, your body still uses energy is respiration, metabolism, breathing, thinking, moving etc. When we work we use energy and burn away at it and we tire. When we dont our body will store energy in our body as fats to use later so we still are using the body resources. However this isnt the main one. We develop a sleep pattern in our lives and our body has a good internal clock that will signal sleep to recharge the brain and body, we need sleep as part of our lives regardless and our body knows that and wants to sleep so we get tired. A solid week without sleep= death no matter how much energy you have, its a biological function. Its more or less our body telling us we are tired and need the rest rather than a lack of energy
Say, why do we feel hungry in the morning even we dont do any work while sleeping. Our body utilizes energy to sustain us, The heart beats because of energy from food, the brain works because of energy. So even we are idle, body utilizes energy to maintain itself, Doing a job like pushing wall makes you feel tired because you consume energy in pushing the wall though its futile to do that, Physics says you didnt do work but you did in biology...isnt it? Enjoy.
it actually depends on how you define work ...

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It's worth noting that when you push a wall you are keeping your muscles in tension. From a physics perspective you are exerting a force on a wall which the wall is equally countering. Energy is being exerted to generate the force so in this case there is work being done despite it appearing like none is being done.
Assuming you define work as force*distance, yes we are not doing any work because we are not actually moving the wall. However, we are still contracting muscles and any contraction, sustained or otherwise, uses up a lot of ATP (the energy storage molecule in cells). In order to replenish the ATP, our body has to metabolize any one of various molecules through glycolysis and aerobic respiration down to (usually) acetyl-CoA which then goes through the TCA (TriCarboxylic Acid) Cycle a.k.a Citric Acid Cycle and the by-products then go to the electron transport chain to produce more ATP. Muscles require a lot of ATP though, so if we hold the push/muscle contraction long enough we will use up the ATP faster than we can make it. We feel tired when we have a low amount of ATP. If you're referring to the tired/sore feeling that lingers for a long while after the push/contraction has been completed that's because the body couldn't provide enough oxygen for aerobic respiration (usually because people were holding their breath) and instead the molecule being metabolized undergoes lactic acid fermentation. The lactic acid causes the sore feeling and because the molecule couldn't be completely metabolized there is actually less ATP produced.

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