|The activities that we do which uniquely symbolize Chanukah are the kindling of Chanukah lights and adding the Al Hanisim prayer in Shmoneh Esrei and Birkas Hamazon. Although we also say the complete Hallel throughout Chanukah, this is not unique to Chanukah, since we also say the complete Hallel on some Yomim Tovim.
It is interesting to note that the act of kindling the Chanukah lights does not encompass any remembrance of the miraculous victory against the Greeks (although there is an opinion that one day of lighting is done to commemorate the victory of war) and the text of Al Hanisim makes no mention of the miracle of the oil. Although we accompany the lighting with the text of "Haneiros Halolu" (Its source is Maseches Sofrim ch. 20.) which does mention the miracle of the war, nonetheless, this is not part of the mitzvoh itself.
Why indeed are these two unique Chanukah activities each bereft of one of the major themes of Chanukah?
We find in Medrash Maasei Chanukah that the Greeks decreed that the Bnei Yisroel may not keep the Shabbos, nor do Bris Miloh, nor announce when the new lunar month would begin or add a new month to the calendar by court injunction - "Kiddush hachodesh v'ibur hashonoh al y'dei Beis Din," and that they may not have doors on their homes. Why did they pick on these specific matters?
An analysis of the Greeks' intention leads us to realize that all of these decrees have a common denominator. The Greeks were not against studying Torah as an intellectual pursuit but were bitterly against the study of Torah which led to a belief that the Torah is a guiding light for people's actions which even reaches into the realm of affecting, mastering over, and even sanctifying the physical. We see this from the text of Al Hanisim, where we say that the Greeks intended "l'hashkichom Toro'seCHO," - to make them forget YOUR TORAH. The Greeks said that the Bnei Yisroel may study the Torah as an intellectual pursuit but not accept it as Divinely given. They may in general fulfill the Torah's commandments, but only as acts of ethnic culture, "u'l'haavirom machukei ritzon'eCHO," - to drive them away from the statutes of YOUR DIVINE WILL. We see this point demonstrated as well further on in the Medrash Maasei Chanukah, which relates that the Greeks told the bnei Yisroel, "Write upon the horn of your ox, - al keren hashore," that you have no portion in the G-d of Israel. On a simple level, this was like having a bumper sticker upon which this declaration would have to be written. In an agrarian society, most people had oxen to till the ground. People spent much time standing behind their oxen while guiding them in the fields and had the ox's horns directly in their view.
However, this can be understood on a deeper level. There is a ruling of "keren hashore." There are financial responsibilities when one's ox or other animal gores another animal or someone's property. If this was done to another ben Yisroel, the financial responsibility is limited to half the value of the damage the first three times this would occur. If however the owner of the ox is a non-Jew, he is responsible to pay the full damage. This irked the Greeks no end. They could accept that the Jews had their unique customs and laws in the sphere of spiritual pursuits, but when it came to the realm of the physical, namely damages of physical properties, they could not accept that the Jews were different because of their being the "people of the book," which permeated even their physical beings and set them apart from all other nations. This is the meaning of write for yourselves "al keren hashore," regarding the law of damages by goring, that you do not have a portion in the G-d of Israel and are no different from us.
Shabbos symbolizes a unique relationship between G-d and bnei Yisroel as stated in the Ten Commandments that Shabbos is a remembrance of the exodus from Egypt which is uniquely a Hashem-bnei Yisroel experience. We stress this in our Shabbos prayers - "Beini u'vein bnei Yisroel ose hee l'olom."
Heralding in the new month or adding a month to the calendar year by an edict of the Jewish court also embodies the concept of the power of the Torah to permeate and master over the physical. There is a physical phenomenon that a girl under the age of three retains her virginity no matter what has been done to her. The Talmud Yerushalmi K'subos 2:1, N'dorim 6:8, and Sanhedrin 1:2 derives from the verse in T'hilim 57:3, "Lo'Keil gomeir oloy" that if a girl had passed her third birthday in the month of Adar and had then lost her virginity, if the court afterwards decides to add an additional month of Adar, this will push her birthday forward by a month, and she slips back to being under three years of age. The moment the court announces the additional month, her virginity physically returns. Similarly, if her third birthday was the first of the month and she lost her virginity on that day and then the court announced that that day would be changed to be the 30th of the previous month, her virginity would physically return. The Greeks could not accept this concept of the power of the Torah mastering over the physical and therefore attempted to abolish the court announcing the new moon or adding an additional month to the lunar calendar.
The Greeks also issued the devastating edict that none of the bnei Yisroel may have doors on their homes. This totally destroyed the honour and privacy of the home and family life. Only after the victory in combat were the bnei Yisroel able to replace the doors of their homes.
Perhaps there was a much deeper and diabolical intention in the Greeks' edict. The Rambam in hilchos mezuzoh 6:1 states that there are ten conditions to be met before one is responsible to place a mezuzoh. One condition is that the doorway must have a door. By prohibiting the bnei Yisroel from having doors on their homes the Greeks effectively negated the mitzvoh of mezuzoh. The Rambam in hilchos mezuzoh 6:13 states that when a person passes by a mezuzoh it should arouse him from his spiritual slumber, bring him back to his senses, and kindle in him a desire to go on a proper path. It also serves as a reminder to not sin, as if an angel is looking on and restraining him from sinning.
The Greeks would not allow the mitzvoh of mezuzoh to be performed, even though all that it is, is a physical piece of parchment and ink, since they understood that it encompassed all that they stood against.
How appropriate it is to light the menorah when it is positioned across from the mezuzoh of the home. The Medrash Mishlei 31:21 says on the words "Ki chol beiso lovush SHONIM," that the word SHONIM should be read SHNAYIM, meaning "in pairs." The medrash goes on to give us examples of mitzvos done in pairs, including the kindling of Chanukah lights and the mitzvoh of mezuzoh. The Medrash Shir Hashirim on the words "Mah yofis u'mah no'amt" (7:6), also pairs the kindling of Chanukah lights with the mitzvoh of mezuzoh.
When our Rabbis give us a mitzvoh related to a happening, they introduce an act that symbolizes the gist of the matter at hand. The miracle of finding oil that was sufficient for lighting for only one day and having it miraculously last for eight embodies the pivotal point of the disagreement between the Greeks and the Torah. The Greeks posited that the physical realm cannot be intruded upon and surely not mastered by the spiritual. The physical limitation of oil sufficient for only one day, yet lasting eight days because the spiritual need required it, saliently laid to rest the thrust of the Greeks' arguments. The spiritual vanquished the physical.
We are to have this concept in mind when kindling our Chanukah lights. The gemara Shabbos 21b says that the lighting of the Chanukah lights should be done while it is noticed by the public. This is expressed as "ad shetichle regel min hashuk, - until pedestrians no longer traverse the marketplace (streets)." According to the concept explained above we can say that one must have in mind when he kindles the lights of Chanukah that Hashem masters over the physical world and it is not left to happenstance, "ad shetichle regel min hashuk," until the thought comes to an end, "shetichle," that the happenings of our physical world are by happenstance, "R'GILUS min hashuk."
The Rabbis therefore instituted the lighting of the menorah as the only mitzvoh of Chanukah. More was not needed as this symbolic reminder of the miracle of the oil encapsulates the victory of the Torah position over the Greek position. There is no need to incorporate anything symbolizing the miraculous victory at war as a mitzvoh act.
On the other hand, in the blessing of "Modim" in Shmoneh Esrei the theme is to give thanks to Hashem for all the good He has done for us. Here giving thanks for the miraculous victory at war is appropriate and there is no need to mention the miracle of the cruse of oil.
This dvar Torah is a compilation of the thoughts of many commentators. Please excuse me for not giving proper attribution.