How can I best communicate I'm a lutheran evangelic as per the German definition?

The Lutheran Church in America has various branches. The Evangelical Lutheran Church in America (ELCA), which is the largest branch in United States, was founded by mostly Scandinavians. In contrast the Lutheran Church Missouri Synod (LCMS) was founded by settlers who came from Germany in the mid to late 19th century.

The LCMS Lutherans tend to downplay the word "evangelical" in describing what they believe. They prefer words like "traditional", "orthodox", "evangelical catholic", "Bible believing" or "confessional" in describing what they believe. The ELCA, which is stuck with the name "evangelical" in their title, is also struggling with brand confusion over that name.

My experience with Lutheranism is mostly with the LCMS branch. Those who have come from the state church in Germany have been welcomed and have felt right at home in the various churches that I have been participated in.

When reviewing the English translation of the German wikipedia article Evangelisch-lutherische Kirchen, "Evangelisch-lutherische Kirchen" is best translated as "Lutheran Protestant Church", or "Lutheran Church" for short, since in English speaking countries, a Lutheran church is automatically Protestant. Therefore it is best for you to identify as a "Lutheran".

As the German Wikipedia article says there are 3 branches of Lutheran churches today, each with their own worldwide organization. In America, the two largest Lutheran denominations are ELCA and LCMS:

• ELCA (Evangelical Lutheran Church in America)is the largest (3.3 million). It is a member of the Lutheran World Federation headquartered in Geneva.

• LCMS (Lutheran Church-Missouri Synod) is the next largest (1.9 million), which is a member of the International Lutheran Council. LCMS should be sharply distinguished from ELCA since it is a lot more conservative (see this article on ELCA vs. LCMS differences).

You are right that "Evangelisch" means "Protestant" and should not be translated as "Evangelical" although all evangelicals are avowedly Protestant (except some, who identify as evangelical Catholics). The Lutheran branch that is closer to Evangelical is LCMS.

Evangelicals distinguish themselves from other Protestants by having 4 primary characteristics (source: What is an Evangelical):

• Conversionism: the belief that lives need to be transformed through a “born-again” experience and a life long process of following Jesus
• Activism: the expression and demonstration of the gospel in missionary and social reform efforts
• Biblicism: a high regard for and obedience to the Bible as the ultimate authority
• Crucicentrism: a stress on the sacrifice of Jesus Christ on the cross as making possible the redemption of humanity

Evangelicals can practice their identity as a member of a historic denomination or as a member of an evangelical church, which distinguish themselves from other Protestant churches:

• Evangelical churches take historic sola scriptura more seriously than liberal-leaning mainstream Protestant churches (like ELCA), leading to a much more conservative positions such as LGBT issues.
• A lot of Evangelical churches in United States are non-denominational.
  • Non-denominational means self-governing, not belonging to a historic mainstream Protestant denomination such as PCUSA (Reformed), Episcopal Church (Anglican), ELCA (Lutheran), United Methodist Church, etc.
  • Non-denominational also means that they are theologically agnostic. An evangelical church can be Lutheran, Anglican, Reformed, Methodist, Pentecostal, etc. as long as they uphold the authority of the Bible and take conservative stance on issues.
• Some evangelical churches DO belong to a loose association or to a denomination such as the Southern Baptist Convention, Assemblies of God, EKD (Evangelical Church in Germany / Evangelische Kirche in Deutschland), etc. See an excellent chart from the National Association of Evangelicals which maps a denomination to theological tradition.
• Historically, the theology of Evangelical churches lean toward Reformed (Calvin), which you correctly identified in German as Reformierte Kirchen. Therefore, Reformed theology is adopted by the majority of evangelical churches today (citation needed).

CONCLUSION: It's best to identify yourself in America as "Lutheran".

• "Protestant" would be fine but as you say, not as distinctive, and may carry a slight negative connotation among Catholics compared to "Lutheran".
• "Evangelical" is another option, only if your theological position leans to EKD and you don't necessarily want to communicate your Lutheran distinctiveness.
• "Confessional Lutheran" is another option if your theological position is conservative, similar to Evangelicals / EKD. This covers LCMS and WELS (the 3rd largest Lutheran denomination in America). See Matthew's answer for more details.

I think the term you want is:

Confessional Lutheran

GratefulDisciple already noted that ELCA has adopted an extremely liberal theology as of late, to the point that they are much closer to "mainstream Protestantism". If you're worried about being tarred with that particular brush, which it sounds like is the case, identifying as confessional Lutheran would be a way to distance yourself from those aspects of Protestantism (and from the extremely liberal ELCA, which is not confessional) that are incompatible with confessional Lutheranism without having to associate with a specific American denomination to which you don't actually belong, and with whom you may or may not be in full agreement.

CLs include LCMS and also WELS, as well as a handful of other even more "niche" denominations (see the Wikipedia article).