How do I go about seeking remuneration from a gas station that sold me bad fuel?

I'm so sorry you've had such trouble with your car as a result of bad fuel.

To answer your questions:

How can you recover your costs?
You should approach the vendor first. They will probably claim (1) no liability, (2) that your recovery is limited to the price of your purchase, or (3) that it's the gas/oil company's fault. You can continue to press them for more money, but I warn you, it will be frustrating and time consuming. Approaching the oil/gas company will be equally as challenging.

Small claims court? Can you do this without a lawyer?
You can file a small claim for money under a certain amount depending on your jurisdiction. Normally, an attorney may not represent you in small claims court. For Pierce County, for example, anything under $5,000.00. A typical small claims court process looks something like this:
1. You complete the Small Claims Court forms.
2. You present the completed forms to the clerk, pay the filing fee, and get a case number.
3. You serve the defendants with the papers. You can't do it yourself, but a friend of legal age can. You wait for a mediation date. This will be 2-4 months from the time you filed your claim with the court.
4. If the other party shows up for mediation, you try to work something out. If you do, you make a contract that binds you both. If you can't work something out, you get a hearing date some time in the future as the schedule allows. In your hearing, the judge will decide who is liable, if anyone, and how much they have to pay in the form of a judgment against them.
5. If the party does not show up for mediation, you get a default judgment. To obtain default judgment, you must also prove that the defendants were properly served with the papers and are not members of the active duty service.
6. When you obtain judgment, in many cases you are required to have the judgment "converted" to a Superior Court judgment so that you can attach to assets. Then you locate the liable party's assets (i.e. real property) that you can "attach" to and force them to be sold (through the Sheriff) so you can keep proceeds to satisfy your claim.

This is a very brief summary of the process. I hope it is helpful.

In the alternative, you can hire an excellent attorney to do all this for you, possibly in Superior Court, and will work with you regarding fees in a way that will work for you. Good luck.