Örebro is a small, historical city in Sweden situated between Oslo, Gothenburg, and Stockholm. It is the self proclaimed "natural logistical centre of Scandinavia". Also it is home to one of Scandinavia's first water towers.
South towards Gothenburg, Malmö
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You can go to Södra station (the south train station in the city center, something about 800 meters south from the main station). There on the street Östra bangatan, you have a busstop where you can stand and the cars going south can stop. Here it is recommendable to have a sign. Another place in the city centre is at Kungsgatan. The street Änggatan is leaving from Södra station. Follow that street approximately 500 meters. When you come to the bigger street called Kungsgatan, go right. After 200 meters, just after the traffic lights, you reach a bus-stop where you the cars can stop.
If you can find someone who will take you to Brändåsen, a big petrol station in the direcction Askersund, about 30 kilometers from Örebro. It is a place where many cars and trucks stops on the way south. It is not recommendable if you want to go to Gothenburg but for the southeastern part of sweden is is good. You can also reach it by bus 841 that leaves from Resecentrum (busstation beside the trainstation) and also passes the busstop at Södra station, a few times every day. The ride is about 70 kronor. Note that you can not pay in cash at the bus. You need to buy ticket at resecentrum.
(edit: info about American car salesman was totally useless. The road doesn't actually go south from there. However, you can follow the footpath under the bridge with the washed-out graffiti (MEGADETH OR DIE) and stand on the road behind that, but there isn't too much traffic that passes through here.)
East in the direction of Stockholm
Go to the main train station. The big road in front of the station is Östra bangatan. With the station building in your back, turn left on the Östra bangatan. Follow the road about 1000 meters and you will have a petrol station on the right side. It is the last petrol station before the exit to the highway. Just after the crossing you have also a bus-stop where you can stand. This place is also good for any direction in the north of Sweden.
At Eurostop in Örebro there's a lot of cars going to Stockholm. When I tried it together with another hitchhiker going south he came back and said that everyone is going to Stockholm and I found a ride before even finishing my sign. You can get there by buses 1 and 2 from Järntorget.