I just did this trip in reverse order. There is a lot of information on each specific border crossing already on the HUBB, so I'll be brief:
Tunisia is easy.
Libya is hard. It's exceedingly difficult (while on the road already) for a westerner to get a transit visa for the country unless you hire a guide. For Polish Citizens, it might work better, but don't hold your breath. If I were you, I would make sure I had the visa in my passport before embarking! Guides are expensive, but perhaps you can split the cost with other travelers.
Egypt is a horrible country... but you will remember it forever! At the major crossing points they have special tourist police who guide you through the painful process of getting your visa and temporary import permit. A carnet is required.
Jordan is easy. Take the ferry from Neweiba, Egypt, to Aqaba, Jordan (to avoid Israel... see the next point.)
There is no way (that I've heard of) to visit Israel with your motorcycle and then continue into Syria. In fact, there is only one land crossing point that allows you to enter and exit the country without a stamp in your passport. The King Hussein Bridge (most direct route between Amman and Jerusalem) is the key to visiting Israel stamp free... but you must leave your bike in Jordan while you visit. And you must leave Israel before your Jordanian visa expires. (Again, there have been many posts on this topic. Search for King Hussein Bridge.)
Syria is no problem. Though they say you must apply for your visa at your home embassy, they will issue it at the border... if there is no evidence of you having visited Israel (including the sticky patch on the back of your passport left behind from an Israeli sticker... peel it off and clean it well!)
Lebanon. Ditto. They are more relaxed than Syria, but they are in a bit of distress at the moment. I'm not sure if or how border crossings have changed there in the past month. (But I am certain that there is no way humanly possible that you can cross from Lebanon to Israel.)
And then you have Turkey. Bingo. QED.
NO problems with Petrol.
Again, avoid Israel unless you can visit it LAST! (It's worth it, but you will not get into Syria if they suspect you've been to Israel! Same with Lebanon, I believe.)