Having a teamsters building near the steel mill would probably help get the steel moving. It will be the closest and fullest building to the teamsters once they come on duty, so it will get their attention. But that's assuming your steel mill is full of steel ready to go. If there's not enough steel there to be a full load it might get de-prioritized.

Insufficient steel at the weapons plant and undelivered steel at the steel mills certainly sounds like an issue with teamsters, though whether it's because you have too few of them or because the ones that you have are spending too long in transit (traffic problem, inefficient road network, et cetera) is something you'll need to assess for yourself.

As to where Teamsters' Offices are best placed, putting the office near a cargo source is probably slightly better than placing it near a cargo sink, but it shouldn't matter too much since teamsters do not need to return to the office between loads and I don't think that the game's shipment allocation algorithm does a whole lot to optimize truck utilization anyways. It's likely more optimal to minimize teamster travel time between home/services and office than it is to minimize travel times between office and cargo source/sink.

I have 2 or 3 teamsters near the factory which is near the dock, I also have 2 or 3 near the steel mill. I have a car factory too that has 2 or 3 teamsters which is near another dock, I was thinking of relocation the Weapons factory to near the car factory, maybe that would help

It's a pity that warehouses aren't very helpful, they only seem good for stockpiling stuff in the Colonial era