Have you received any documents titled "Notice of Enforcement"?
Before the bailiff can enforce their warrant they need to serve a Notice of Enforcement for each PCN on you at the address where you live. Not some previous address. The Notices must give you seven clear days to pay. The day of issue, Sundays and bank holiday's are not clear days.
The normal first visit tactic is to clamp your car and demand immediate payment to release it. An additional £235 fee is levied when they visit. Regardless of whether they found your car or not.
If you have a car parked on a public road, then I suggest you move it somewhere else. Into a garage, if you have one or on somebody else's property, friend or relative. Don't just park round the corner or the next street.
Don't let the bailiff enter your property. And they have no power to force entry. But they will try and bully you into letting them in.
For advice on handling bailiffs you could try
Bailiff Advice Online. You sound like you may fall into the vulnerable category in which case the bailiff has to take this into account. BAO can advise.
You should also advise the bailiff that a Statutory Declaration and or a Witness Statement has been filed with the Traffic Enforcement Centre at Northampton County Court and that any enforcement should be suspended pending the Court's decision. Also inform the Council, that might be difficult and frustrating, and ask then to call off the bailiff pending the outcome of the SD and/or WS.