You can take the train which will take about 2-3 hours with a couple of changes. Go to http://www.bahn.de/i/view/GBR/en/index.shtml and look for the connections between Munich Airport and Straubing.
You can rent 2 cars or try and rent a nine-seater and drive to Straubing which is about 100km away from Munich airport. Then either keep it for the duration of your stay or return it to the car rental office in Straubing on the same day (I think Hertz, Europcar and Sixt have an office there).
You can also try and get a taxi transfer, not sure how much this will cost though I am guessing it will be about 200 EUR. Renting or taking a taxi may actually not be much more expensive than taking the train as you are 8 people.
Another alternative could be to fly in to Nuernberg and rent a van from there. The distance to Straubing is about 150km.
Flying to Munich is almost certainly the quickest way to get to Straubing.
Easyjet or Lufthansa flights takes about 2 hours. From Munich airport to Straubing by bus and train takes between 2 hours to a little over 3 hours depending on the train schedule connections. Take the bus from the airport to Freising, then the train to Plattling, where you change for Straubing. There is an alternative route that takes you from Freising to Neufahrn (Niederbayern) where you can also change for Straubing. In terms of time there's little in it. Once you know your flight arrival time, use the bahn.de site to see the various train options.
You can do the entire bus/train journey using Bayern-Tickets, assuming you use only regional trains. For 8 of you, you will need 2 tickets (2x4 people- total cost 70€). Bayern-Tickets can be bought from the ticket machines at the airport on the day. Make sure that someone signs each ticket to validate it.
The journey time by car is just over an hour, via the A93 Autobahn as far as the Landau an der Isar exit, where you pick up the Landestrasse 20 to Straubing. If time is the most important factor, then hiring a couple of cars or a small transit type vehicle will certainly be the quickest, but not the cheapest method.
Germanwings fly Heathrow to Nuremberg. From the airport take the U-Bahn to the Hauptbahnhof. From there take a train either to Regensburg or Neumarkt (depending on time of day then change for Straubing. Journey time between 2 hours 15 mins to 2 hours 35 mins. Bayern ticket works for this route as well as the Munich one.
It's also possible to do the entire from London to Straubing by train, with changes at Brussels and Frankfurt. This can cost as little as 59€ per person, each way. The journey will take anything from 10 hours upwards, depending on connections. Tickets are only valid for specific trains, so if you miss a connection you need to go to the ticket office to get the ticket revised. Tickets can be purchased via http://www.bahn.de/i/view/DEU/en/index.shtml. up to 92 days in advance. But the 59€ tickets tend to sell out very quickly.
Just seen this thread!
6 of us are going to Straubing in August and the place we are staying st us up with a taxi firm...here the email address: firstname.lastname@example.org
€120 one way and it'll take around 45 minutes.