How practical would it be to install a micro-sized overhead power line? It's to get power to a part of the yard where underground power would be too tricky to install.
Also, it would be like 25 feet and only 120 volts.

Well what I would do is get some wire and stretch it from Point A to Point B
Of course give the wire some slack for the changes in temperature
Otherwise I really didn’t get what you were talking about. What’s micro sized//like a smaller version of a real power line?

What’s micro sized//like a smaller version of a real power line?

This micro power line is like the power lines that feed your house from the transformer, but it's not as bulky as those ones.

How practical would it be to install a micro-sized overhead power line? It's to get power to a part of the yard where underground power would be too tricky to install.
Also, it would be like 25 feet and only 120 volts.

An outdoor cable for suspended installation (with the required accessories)...
This is not so unusual problem, so well supported in any Code (wherever you live; the Code describes how to do that correctly)...

The other question is, how not to screw up Earthing

Just connecting together the house Earth with strong remote Earth (metal shed, ...) through the 1.5mm^2 PE core of the cable may subject the 1.5mm^2 core to excessive stray currents, which will pose a fire hazard

The other question is, how not to screw up Earthing

Just connecting together the house Earth with strong remote Earth (metal shed, ...) through the 1.5mm^2 PE core of the cable may subject the 1.5mm^2 core to excessive stray currents, which will pose a fire hazard

I could run the cables to a junction box with a grounding rod, and I think that will provide a good earthing connection.

The problem that could arise is, if you interconnect 2 good Earth connections which are stuck into the Earth at some distance from each other

There may appear currents coming from the electrical installation (e.g. the house, the neighbors via grid Neutral and TNC-S Earth-Neutral connection in the house, etc) or from the Earth and through the Earth core of the cable. Such currents are hard to predict and might exceed the ampacity of the cable, especially if it is a thin cable

The earth conductors (in an ideal world) are not going to be connected to the power lines unless it's the main panel (which the overhead circuit won't have), and the grounding rods are only going to be about 50 feet away from each other anyway.

For a permanent installation, I would use standard triplex cable (such as this, the smallest this company makes is 6AWG but others might offer something smaller). It would be expensive, but very durable. It is the same style as the service drop from the utility to your house. I would use insulated anchors at both ends to support the bare neutral like the power company does, and use weather heads at both ends with conduit for the connections. Around here, the power company uses one that has one hot and the bare neutral only for small circuits such as street lights. Typical service drops are larger and have two hots (for 120/240V) or three for three phase.

I don't know what is your budget, but this proposition could be more expensive than an underground feed, depending on who you would hire to dig the trench.

The Earthing system used in the US and in most of the world is called TNC-S. In this system, the "Neutral" from the grid up to the panel is actually a wire that combines 2 functions : Neutral (for handling load current) and Protective Earth (for closing the fault circuit in case of L-PE short). This wire is called PEN (PE and N). Since it is an Earth wire, it can be bare

At the panel (the main one) the PEN is split into PE and N wires. From here on, they have separate tasks : PE only for protection, N only for load current. The N is not Earth anymore and therefore cannot be bare. Also, even though PE and N are connected together at their beginning, they cannot be connected together again anywhere on the circuit

If you take N from the panel as N, you can't do with it anything that's permissible with PEN or PE wires. so it can't be bare (even in the overhead), it can't be connected to any metallic enclosures etc

If you take PEN from the panel, there applies a whole set of requirements for the cable and for the remote Earthing, which may be not practical to comply with for a small line (it makes sense to comply with them only when the heavy gauge cables are required anyway for the load current, or when TNC-S is specifically wanted for better protection against e.g. lightning). If you aren't going to comply with them, then you can't pull PEN but only N, and must care of the Earth connection in other ways

You need special overhead wire for that, use Undergroud feeder underground.

The Earthing system used in the US and in most of the world is called TNC-S. In this system, the "Neutral" from the grid up to the panel is actually a wire that combines 2 functions : Neutral (for handling load current) and Protective Earth (for closing the fault circuit in case of L-PE short). This wire is called PEN (PE and N). Since it is an Earth wire, it can be bare

At the panel (the main one) the PEN is split into PE and N wires. From here on, they have separate tasks : PE only for protection, N only for load current. The N is not Earth anymore and therefore cannot be bare. Also, even though PE and N are connected together at their beginning, they cannot be connected together again anywhere on the circuit

If you take N from the panel as N, you can't do with it anything that's permissible with PEN or PE wires. so it can't be bare (even in the overhead), it can't be connected to any metallic enclosures etc

If you take PEN from the panel, there applies a whole set of requirements for the cable and for the remote Earthing, which may be not practical to comply with for a small line (it makes sense to comply with them only when the heavy gauge cables are required anyway for the load current, or when TNC-S is specifically wanted for better protection against e.g. lightning). If you aren't going to comply with them, then you can't pull PEN but only N, and must care of the Earth connection in other ways

I should have been more clear, the overhead power line will only have hot and neutral wires, the grounding system at the other end will be isolated from the main one.

I have a couple bugzappers that I put up in what's sorta the center part of the yard...for power I just run an outdoor extension-cord under a 1x2 board on the ground (so the top of the board is flush with or slightly below ground-level)...no chance of tripping on or mowing it that way

Yeah I probably violate some rule somewhere, but simple fact is its a temporary 'install' not something permanent.  I don't leave it out all year, at the point in fall where things have cooled off, the cords & bugzappers all go back in the shed til sometime in mid/late spring.

The thought of stringing a cord of some sort through the air did cross my mind, but I also consider something like that very tacky looking .lol. (and less safe than what I do)

I should have been more clear, the overhead power line will only have hot and neutral wires, the grounding system at the other end will be isolated from the main one.

For your case my post means, that while the power company can use bare wire for the Neutral in their service drops, you cannot do the same in yours. You must use isolated Neutral

For your case my post means, that while the power company can use bare wire for the Neutral in their service drops, you cannot do the same in yours. You must use isolated Neutral

The problem is, the only overhead cables available all have a bare neutral wire.