Affectionately known as Reb Shaya'le (Rabbi Yeshaya Steiner of Kerestir), the Kerestirer Rebbe lived around the beginning of the 20th Century. He was a very pious man and extremely humble, always referring to himself in the diminutive (Shaya'le). He was known as a "miraculous" person. His greatest pleasure was to host a very elaborate Melave Malka, the meal that follows Shabbos, on Saturday night. Often he would have his chassidim shecht fresh chickens for his meal.
One motzo'ay Shabbos, while Reb Shaya'le was eating this special melave malka meal, a chossid came to him with an urgent request. He was a man who had a warehouse full of foodstuffs and he made his living by buying an selling food. For the past number of months, his warehouse had been taken over by mice who were eating his grain and other commodities and his entire livelihood was threatened. He asked Reb Shaya'le for a blessing that the mice should leave his warehouse. At that time, each small town in Europe was ruled by the local church pastor. Some of the pastors were kind towards the Jews and others were very harsh. Reb Shaya'le asked the chossid if the pastor of the town he lived in was kind or harsh. The chossid replied that he was very harsh toward the Jews. Reb Shaya'le then instructed the chossid to go to his warehouse and to tell the mice, "Reb Shaya'le says to go to the estate of the pastor." The chossid followed the Rebbe's advice and instantly hundreds of mice raced out of the warehouse all heading in the direction of the pastor's estate. The chossid's business was saved and ever since Jews who have been plagued with this problem have used Reb Shaya'le's picture to accomplish the ridding of mice from their homes. - Reb Shayele - Stories (jewishgen.org)
The story behind the segula of Rav Meir Baal HaNes has its basis in Mesechtes Avodah Zarah 18a-b of the Talmud.
When Rabbi Meir’s in-laws were found teaching Torah publicly, they were executed and his sister-in-law was taken by the Romans. Determined to win her release, Rabbi Meir took a large bag of golden dinars and approached her warden with the bribe. “Take the dinars, and give her to me!” he demanded. The warden, fully aware of his fate should the escape be discovered, refused. Rabbi Meir then instructed him that if his superiors would try to harm him, he need only cry out, “G-d of Meir, answer me!” and the threat would disappear. The warden was skeptical, so Rabbi Meir proved the efficacy of the segula by throwing a stone at the vicious jail dogs. When the dogs rushed to attack him, Rabbi Meir cried, “G-d of Meir, answer me!” and they retreated meekly. The Roman warden, satisfied that he could rely on the miracle, released the girl. Sure enough, her disappearance was quickly discovered, and the guard was taken to be hanged. At the last moment, he exclaimed, “G-d of Meir, answer me!” The executioner suddenly stopped, took him down from the gallows, and questioned him. When the guard revealed the entire episode, the Romans engraved a likeness of Rabbi Meir on the city gates and hunted him down as a wanted man. Rabbi Meir narrowly escaped, but felt it necessary to run away to Babylon to avoid the Romans. - Prayer for Lost Object | The Story Behind the Segula | Kupath Rabbi Meir Baal Hanes
אֵין מְנַחֲשִׁין כְּעַכּוּ''ם שֶׁנֶּאֱמַר (ויקרא יט כו) "לֹא תְנַחֲשׁוּ"... וְכֵן הַמֵּשִׂים סִימָנִים לְעַצְמוֹ אִם יֶאֱרַע לִי כָּךְ וְכָךְ אֶעֱשֶׂה דָּבָר פְּלוֹנִי וְאִם לֹא יֶאֱרַע לִי לֹא אֶעֱשֶׂה, כֶּאֱלִיעֶזֶר עֶבֶד אַבְרָהָם. וְכֵן כָּל כַּיּוֹצֵא בַּדְּבָרִים הָאֵלּוּ הַכּל אָסוּר. וְכָל הָעוֹשֶׂה מַעֲשֶׂה מִפְּנֵי דָּבָר מִדְּבָרִים אֵלּוּ לוֹקֶה:
It is forbidden to practice enchantment as the idolaters do, even as it is said: "Nor shall ye use enchantment" (Ibid. 19.26)... So, too, is one who sets certain signs for himself to regulate his actions, saying: "If such thing will come to pass I shall do that thing, but if it will not come to pass I shall not do it", even as Eliezer, Abrahams servant did. And so are all like practices of such things forbidden. And whosoever commits an act as a result of any one of such practices, is lashed.
וְכִי נָחָשׁ מֵמִית אוֹ מְחַיֶּה? אֶלָּא, בִּזְמַן שֶׁהָיוּ יִשְׂרָאֵל מִסְתַּכְּלִין כְּלַפֵּי מַעְלָה וּמְשַׁעְבְּדִין אֶת לִבָּם לַאֲבִיהֶם שֶׁבַּשָּׁמַיִם הָיוּ מִתְרַפְּאִים, וְאִם לָאו הָיוּ נִמּוֹקִים (ראש השנה כ"ט):
Our Rabbis said: But could the copper serpent cause death or life?! But the explanation is that when the Israelites in gazing at the serpent looked up on high and subjected their hearts to their Father in Heaven, they were healed, but if they did not do this they waste away (Rosh Hashanah 29a).
תָּנוּ רַבָּנַן: שִׁשָּׁה דְבָרִים עָשָׂה חִזְקִיָּהוּ הַמֶּלֶךְ, עַל שְׁלֹשָׁה הוֹדוּ לוֹ, וְעַל שְׁלֹשָׁה לֹא הוֹדוּ לוֹ. עַל שְׁלֹשָׁה הוֹדוּ לוֹ... כִּתֵּת נְחַשׁ הַנְּחשֶׁת — וְהוֹדוּ לוֹ...
The Sages taught: King Hezekiah performed six innovative actions. With regard to three the Sages agreed with him, and with regard to three they did not agree with him. With regard to three actions the Sages agreed with him...
He ground the copper snake through which miracles were performed for Israel (Numbers 21:9), destroying it because it had been used in idol worship (II Kings 18:4), and they agreed with him.