This is a brief try at creating an OOB for the IDF units involved in the ground offensive in Gaza as part of Operation Protective Edge. As usual, everything is based on open sources, mainly published in English.
To begin with, as noted earlier, Haaretz listed that three brigades were mobilized on the border as part of the calling up of over 50 000 reservists. However, a far larger number of units involved in the fighting has since been identified. My guess (keyword) is that two task forces have been created around the Nahal and Golani brigades respectively, in the tradition of the Israeli Ugda (the IDF take on a divisional combat team, usually somewhat smaller than a regular division, but varies greatly in size depending on the mission). Units identified so far:
Golani Brigade: Hebrew: גולני. Often seen as the premier Israeli infantry brigade, it has seen battle in all of Israel’s major wars since its independence in 1948. In recent times, the brigade not only fought in the Battle of Bint Jbeil in 2006, described as the heaviest fighting in the Second Lebanon War, but also took part in Operation Cast Lead, the IDF incursion into Gaza in 2009. During Cast Lead, it was also deployed to the northern parts of the Gaza Strip, meaning that at least for some of the officers, it is a familiar battlefield they are coming back to.
Having met the hardest resistance, the unit has also suffered numerous casualties. An APC attached to the unit was destroyed in a widely publicized incident in the hard battles in Shejaia, with the brigade losing 7 soldiers, the body of one still being unaccounted for. It has been claimed the vehicle was a Zelda (M113), but this is unconfirmed as remarkably little details of the incident has surfaced, and I have not been able to find any photos of the wreck.
Among the brigade’s wounded are two high-profile cases, namely the (unnamed) commander of the Egoz Reconnaissance Unit (Hebr. Yehidat Egoz), the brigade’s special forces unit, as well as the brigade commander himself, Col. Rassan Alian, who suffered light-to-moderate shrapnel injuries, including to his eyes, but sources claims his vision was undamaged. He has since returned to Gaza to resume command of the unit. Of note is that Col. Alian is not Jewish, but an ethnic Druze.
Nahal Brigade: Hebrew: הנח”ל. Alternative transcription Nachal, is an infantry brigade which has its roots in the Nahal movement, which was a youth program created by Israel’s first (and very much socialist) prime minister David Ben-Gurion, where young people combined agricultural work and setting up new farming villages with military service. The brigade itself was created in 1982, and while the current brigade is more “standardized”, it still maintains a somewhat unique character through the inclusion of a large number of foreign volunteers (Hebr. “Mahal”), as well as having a battalion focusing on integrating soldiers from lower socio-economic communities into the army.
While this might sound like an unlikely candidate for use as part of the frontline troops, the Nahal also has a good track record in combat, tracing its roots to the Nahal airborne battalion which prior to 1982 fought as a reserve unit in the paratrooper brigade. As such, it counts the battles of the Mitla Pass in 1956 and unification of Jerusalem in 1967 amongst its traditions. The special nature also ensures that it has a cadre of volunteers with high morale, and in addition to the Second Lebanon War it has served in the West Bank, thus becoming familiar with fighting in an urban environment.
Additional units: A number of additional units are also in the general area, either operating in support of the infantry brigades, or securing the Israeli side of the border.
Paratrooper Brigade (Tzanhanim): Hebrew: הצנחנים. After going into battle by jumping out of plane went out of style, the IDF paratrooper brigade has been used as an elite light infantry unit in all wars since the Suez Crises of 1956 (where it performed its one and only operational combat jump). So far little has been leaked about the employment of the brigade, and the losses reported have been light. Picture number 4 in this slide show places their staging area in Sderot, and apparently they are supported by M113’s. However, this article places at least some paratroopers in northern Khan Yunis. This might indicate that the brigade is split into smaller components to provide added infantry support to the infantry brigades as needed.
401st “Iron Trails” Armored Brigade: Hebrew: הברזל. The unit is confirmed to be in Gaza. During Operation Cast Lead, the 401st led the advance through central Gaza Strip, and reached the Mediterranean Coast, cutting of Khan Yunis from Gaza City. The main equipment of the brigade is the modern Merkava 4 MBT, protected by the Trophy active anti-missile system. The article quoted earlier gives the impression that they are operating close to El-Wafa Hospital, which would place them in Gaza City. The natural place for the brigade would be the gap between Gaza City and Nuseirat, opposite Netivot, the same area where they operated in Cast Lead. It is also possible that the 401st is operating in an idependent role. The Armored Corps lost two company commanders Tuesday evening (22nd of July), at least one of whom fell to sniper fire, but it is unknown if they came from the 401st or if more units are in the area.
The Engineering Corps are naturally heavily involved, intermixed with regular units. At least one soldier from the Engineering Corps has been reported as a casualty. This happened in the central Gaza Strip, and it is mentioned that his Puma heavy combat engineering vehicle was hit by anti-tank rocket fire.
The Givati Brigade, the brigades of the territorial Gaza Division, and the officer training base Bahad 1 have all taken part in some fighting, with the commanding officer of the Gefen Battalion of Bahad 1, Lt.-Col. Dolev Kidar, being killed in action during a tunnel infiltration by Hamas terrorists ,  & . Most likely these units are deployed to guard against Hamas infiltration attempts.
The Artillery Corps are supporting the operation with M109 155 mm self-propelled howitzers.