All right - I am no expert on this, but I'll try my best to help you out a bit.
Note that I will also change the spelling of some of your terms.
OrdnungsPolizei = civilian police
Ordnungs
polizei = originally civilian police. Troops intended for guarding important places or lines of communication. Also used for mopping-up operations and security in the hinterland.
Feldgendarmerie = military police
That's it.
Infanterie Group = Rifle squad
For this, you need context. Group translates literally to Gruppe. A "Gruppe" is the equivalent of an (infantry) squad. The squadleader would be called the "Gruppenführer", literally group leader. You will hardly find a denomination smaller than the company (Kompanie) in official records. Smaller units such as the 'Zug' (Platoon), 'Gruppe' (Squad), or 'Trupp' (Halfsquad) are mentioned, this mostly serves the purpose to give an idea of the number of men involved.
Mostly in combination with a name, such as 'Gruppe Döring', what is meant would most likely be the short form of 'Kampfgruppe Döring'.
Kavallerie = cav squad
Kavallerie is just the general term for cavalry. In the cavalry (Kavallerie), the unit denominations differ from those in the infantry or artillery. The same is true for the denominations of the military ranks. Military units that were originally cavalry kept these denominations after being restructured, i.e. the 24. Panzer-Division, formerly a cavalry unit, would still use cavalry denominations and ranks.
The equivalent of the company (Kompanie) would be the squadron (Schwadron) in the cavalry. The equivalent of the platoon would be the "Reiterzug", the equivalent of the squad would be the "Reitergruppe", the equivalent of the halfsquad would be the "Reitertrupp". Something similar like the "Reitertrupp" is the "Reiterabmarsch", the "Reiterspähtrupp" (cavalry recon halfsquad), and the "Reiterfeldposten" cavalry picket in the size of roughly a halfsquad or squad.
Kradschutzen = motor cycle squad (6 men) with MG 34 LMG
Kradsch
ützen = general term for infantry on motorcycles. "Krad" is short for "Kraftrad", i.e. motorcycle.
Kradschutzen sw = motor cycle squad (6 men), 5cm GrW 36, 4x Kar 98k, 2x MP 28 SMG
"sw" or "s" is the abbreviation for "schwer", i.e. heavy. As opposed to "m" for "mittel", i.e. medium and "le" or "l" for "leicht", i.e. light.
3xBeiwagenKrad = ?
Beiwagen Krad means motorbike with sidecar
leichter Infanterietrupp = light rifle squad
light infantry halfsquad. In general the 'Trupp' was the smallest subunit in the Wehrmacht. It could number between roughly 3 to 15 people, depending on its tasks. An Infanterietrupp would be a halfsquad. A Funktrupp would be the radio-crew. Some specialized units would often be a "Trupp", for example a "Druckerei Trupp" responsible for printing things within a Division. You get the idea.
Infanterietrupp = rifle squad
infantry halfsquad, would be commanded by a 'Truppführer', which is not a military rank but a designation. In case of an MG this would be a 'Gewehrführer', in case of a gun a 'Geschützführer'.
schwerer Infanterietrupp = heavy rifle squad
heavy infantry halfsquad
Angriffstrupp = assault squad
assault halfsquad
Aufklarungsabteilung = recon rifle team
Aufkl
ärungsabteilung. This is a recon unit, but it is much larger than a rifle team.
The equivalent of the 'Bataillon' in artillery, armored, and recon units is the 'Abteilung'
Pionier truppe = engineer squad
Pioniertruppe. "Pioniere" can be construction troops or assault engineers. "Truppe" means branch of service and is not to be confused with "Trupp" which is rougly a halfsquad
Bruckenfahre-Trupp = bridge-ferry squad
I can quite get the meaning of this Brückenfahr-Trupp. It sounds like it has something to do with bridges and it must be a small unit being a 'Trupp'.
So did the Germans use:
Leichter Infanterie Truppe or Leichter-Infanterie-truppe or Leichter-Infanterietruppe
None of that.
Leichte Infanterie-Truppe. This would be a general term like light infantry forces.
Some early German divisions in North Africa would qualify or Jäger Divisions.
Or was it Gruppe?
"Gruppe" means squad in infantry units. In the Luftwaffe, however, designates a larger flying formation.
Likewise was recon troops/scouts called:
Aufklarungsabteilung or Spaehtruppe
Aufkl
ärungsabteilung, Sp
ähtruppe. As for the Aufklärungsabteilung, see above. That would be a recon unit of battalion size which would be part of a division. 'Spähtruppe' is not to be confused with 'Spähtrupp' - see above under your query Pionier truppe for the difference between 'Truppe' and 'Trupp'. A 'Spähtrupp' would be a small recon unit. For example a 'Panzerspähtrupp' of an infantry division would consist of two armored cars. An infantry 'Spähtrupp' would have the size of a halfsquad or squad.
Same with the Infantry, was it:
Infanterietrupp or Infanterie gruppe
"Gruppe" is a squad. "Trupp" is roughly a halfsquad.
von Marwitz