The question above is very simple and up to this point I had thought the answer to be yes, but I've got a debate running on the topic. A fellow player believes that no, they are not Strength checks, primarily because they are part of Bull Rush and Trip and have size and stability modifiers, and are thus no longer plain strength checks, which would be 1d20+Str.

So, are they actually Strength checks like they say they are? And specifically, do effects that boost Strength checks boost them like I think they do?

I'm not sure if there is an official ruling on it or not, but it seems likely that a Strength check with modifiers is still a strength check. Otherwise, it would seem that the effects that boost Strength checks would cause the Strength checks to no longer be Strength checks, and thus not qualify for the boosts.

yes they do. If your str is increased by Rage, or some other boost, your checks are therefore increased as well as it states that you make a Str Check modified by those other factors such as extra legs and size.

http://www.d20srd.org/srd/combat/spe...s.htm#bullRush - Str check.
http://www.d20srd.org/srd/combat/spe...tacks.htm#trip - Str check.
http://www.d20srd.org/srd/combat/spe...cks.htm#disarm - Opposing attack roll.
http://www.d20srd.org/srd/combat/spe...ks.htm#grapple - Opposed attack roll.
http://www.d20srd.org/srd/combat/spe...ks.htm#overrun - Str check.
http://www.d20srd.org/srd/combat/spe...cks.htm#sunder - Opposing attack roll.

I don't really understand the question. I mean, if the rulebook says Str check then it is a Str check. What's there to debate about?

The debate is that a Trip attempt calls for a strength check, yes, but it's not called a strength check, it's called a Trip attempt.

You said it yourself, the trip attempt calls for a strength check as part of the maneuver. Any modifiers that apply to any strength check apply to that. However, they wouldn't apply to the initial melee touch attack unless they also normally apply to melee touch attacks.

I've done Judo in the past and can attest that a trip attempt, as far as most martial arts are concerned, is not about strength. It's about balance and timing which would be better suited in the Dexterity column if you ask me.

And I've tripped a dude by just kicking his legs out from under him, with no skill. In the end, you could be better or worse or skilled or not, the act of knocking someone to the ground with a kick, grabbing their ankles, using a flail even, it's all still strength. Improved Trip, the touch attack and opposition by Dexterity emulate many functions of the skill you can use, but there's nothing in the rules that says tripping someone isn't a Strength check and at least three examples that say it is Strength.

Ultimately if its your campaign you get to adjudicate it any way you like. I could argue that 'kicking' someone is not a trip but an attack, which would be primarily strength. That said, unless you wanted to administer each trip based on the technique used your probably just better off sticking with the canon rules as is. Then again Ive seen small guys sweep much bigger guys and I can be pretty sure it had nothing to do with strength. In fact, if your trying to muscle through it your probably doing it wrong. Just my .02 though.

I think it's better to describe them as strength plus leverage. While dj2145 is correct that strength isn't everything, it's still important and so a stronger combatant is a better one, skill being equal. Being larger means you have a broader base as does being a quadruped. This gives you better leverage for your strength score.

So Trip and bullrush are based upon strength and have factors that effect leverage.