Shraga was born in Bratislava, then in Czechoslovakia, to Leah née Kramer and Mordechai Levinger. The family had four children: three sons, of whom Shraga was the youngest, and a daughter, the baby of the family.
The family was well-off, religious and fervently Zionist. The father was a merchant. When Hitler took over Germany, the parents decided to leave home and make aliyah. First came the father as a tourist, finding a family which was unsuccessful in the Land of Israel, whom he paid generously so they could relocate elsewhere, while he took their passports. Even though this passport only listed three children, the Levinger family was able to reunite in the Land of Israel after a few months, in 1934.
The family lived in Tel Aviv, and Shraga studied in Tachkemoni School and in Yeshivat Tel Aviv. In late 1945, while he was still a yeshiva student, fifteen-year-old Shraga joined the ranks of Lehi. He was not the first, nor was he alone. All of the children, encouraged by their parents, were active in the underground. Meir, the firstborn, was an officer in the War of Independence killed in action; he started out in the Hagana, but with his disappointment at its inaction, he joined Lehi. The second brother, Yaakov, and the baby of the family, Malka, were active in the ranks of IZL. The parents allowed them to host and hide wounded and fugitive members of the underground. The mother even made glue so they could put up posters.
Shraga’s first job was putting up posters and disseminating materials. Afterwards, he worked on gathering intelligence, observing from various spots the movements of the British Army, as well as following Jewish groups who opposed the underground. Naturally, shortly after the establishment of the State, on 29 May 1948, Shraga enlisted in the IDF, before he turned eighteen. He was together with his underground comrades, joining Battalion 89 of 8th Brigade. He was the communications sergeant for Company B, a half-track company composed mainly of the Hagana’s special company and Mahal foreign volunteers. Shraga fought in every one of their battles in the War of Independence.
After his service, Shraga completed his matriculation and pursued further academic studies. He graduated from Hebrew University with a degree in political science and international relations. He worked in industry for decades, managing human resources and serving in an executive capacity until he retired in 1995.
In 1953, Shraga married Anavit Cohen, formerly of IZL. They had two sons, Eran and Yoram, as well as grandchildren. Shraga was active in the Am Yafeh, Am Ehad organization, as well as the Friends of the Surgical Department of Ichilov Hospital in Tel Aviv.