Sure, pay off your car loan if there is no penalty for doing so.
Keep your expenditure under control in case you have a dramatic fall in income.
You have €660k in assets and €700k in liabilities.
If you save €10k and pay it off your mortgage, you will have €660k in assets and €690k in liabilities, i.e. a defict of €10k.
If you put the €10k on deposit instead, you will have €670k in assets and €700k in liabilities i.e. you will have the same deficit.
It makes no sense to pay off your commercial loan. You are paying 1.9% gross. you are getting around 50% tax relief on 50% of the interest, so the net cost is around 1.5%. You can get far more than this after DIRT on deposit, so it makes more sense to put your money on deposit.
This also has the advantage of being accessible if you do lose your job and need the money.
If you do want to reduce your mortgage, reduce the mortgage on your home first. This attracts much less tax relief than the commercial property. It is the combined negative equity which matters, not the distribution across the two properties.
See this
Key Post about investing or paying off your mortgage.
The biggest issue for you is to decide whether you should keep your investment property or not. You are exposed to a number of risks:
1) Interest rates will rise
2) You may have difficulty renting it or collecting the rent.
3) If it falls further in value, it will exacerbate your situation if you do have to sell it. (I am not predicting a fall - I am just pointing out that it is a risk which you should not be taking).
Given the size of your debts relative to your income, I think that you are overexposed to the property market and should sound out putting it on the market. If you don't get a good price, don't sell.
Let me put it another way, if you had a home worth €300k with a mortgage of €340k on it, would you borrow another €300k to buy a property for €300k? Of course, you wouldn't.
Brendan