The House of Strolheim has a bloody, harsh past. A noble house located in Germany, Strolheim has always been a symbol of power. Ever since roughly 1500 AD, Strolheim was both a noble house and a top-notch mercenary unit, fighting for the highest bidder. The leader of the House would by tradition raise a child to be their heir, and when the heir was ready to take over the House, they would slay the current leader in honorable single combat.
Wolfgang Krauser changed that, in recent history. Having killed his father in a fair fight, Krauser made sweeping changes to the House's focus and goals. He suspended all mercenary operations, instead making Strolheim a haven for promising fighters; a gathering of both proven talents, and likely prospects. Krauser's goal is to increase his own power through training against such people, as well as improve their own abilities; a growth of power for all, more or less.
While training in the House is often quite rough and demanding, it is rarely brutal. Krauser is not afraid of killing, but he is not a monster and does not feel failure should merit death. Anyone that he invites to join the House has real promise as a fighter, and it would be a waste to kill them just because they lack the vast experience and talent some people have.
Generally, Strolheim as a group is content to simply remain nested near the Strolheim Village and Castle in Germany. There, they train, and promote the spread of power, as well as how to be responsible in using said power. They want everyone to improve themselves, so that humanity as a whole becomes better and better.
As a result, Strolheim usually stays out of world affairs, working with groups of individuals rather than trying to influence entire nations on the political level. However, there are groups whose actions or ideals clash with Strolheim's, and so Krauser and his followers sometimes target these groups.
Shadaloo is one of these enemies. Strolheim is one of the few groups that knows of Shadaloo's tendency to abduct certain types of young people for use in the Doll Project or brainwashing experiments. Krauser not only finds this morally reprehensible, but also directly damaging to his goals, and so the House of Strolheim often attacks Shadaloo in the field when the chance arises.
The Southtown Syndicate is another major enemy. The Syndicate's ruthlessness in dealing with people who interfere in their plans often results in death or serious injury to good-hearted fighters who did the right thing, but simply took on an enemy too large to deal with. These deaths and injuries also stunt the "growth of talent" Strolheim desires, and so Strolheim sometimes attacks the Syndicate when the opprotunity presents itself.
Finally, Kain R. Heinlein and Grant are another notable group of foes. Kain and Krauser are opposite sides of the same coin: both desire to see humanity be improved, but they go about it in different ways. Kain prefers to recruit those who are already strong, and kill the weak. Krauser prefers to build up the weak, or at least ignore them in favor of others, and so their idealogies clash often.
Getting into Strolheim is difficult. Krauser must be greatly impressed with an individual in order to invite them to join, as only those with strong personalities and real potential to excel get his attention.
Ultimately, Strolheim will likely remain a small group. Their 'army' consists solely of talented fighters, and despite Krauser's wishes to improve everyone, he knows that adding the currently unmerited to the group would dilute the quality of training for everyone there. So for now, Strolheim remains an "Elite Club."