Having read through all of this, I'll give some thoughts.
First, you are describing a situation akin to alien invasion. A small group of extremely advanced aliens attacks a civilian target without warning. I don't know that your raiders
actually are aliens, but that was how I interpreted things. If this is not the case, you'll need to make sure your readers know these are humans. You'll also need some very convincing evidence as to how such a vast technology difference came to exist between the US (or any comparable modern nation) and this raider faction.
I can see no reason for the raiders to abduct random local civilians unless they have absolutely no information on the defenders. AKA alien invaders. Politically speaking, they may try and exchange hostages, but if this is an opening salvo, the defenders are unlikely to have prisoners of their own, and the raider tactics prevent any from being taken in this engagement. Besides, with this level of technical superiority, I can imagine the raiders could mount impressive special ops forces and forcibly retrieving any captives from the defenders.
If they are indeed lacking information about the defenders for some reason, they should be looking at the internet, not mounting raids. With their level of technology, I would expect they can find an internet cafe. Heck, they could probably hack into a sizable number of secure databases without even getting out of their PJs. They'd only need to conduct raids to access closed systems (such as highly-secure military installations).
As others said, I cannot imagine 500 defenders could force military victory against this highly-superior force of raiders. However, the defenders don't need to; if the raiders accomplish their goals, whatever they are, the raiders will simply leave on their own. The defenders could claim it as a victory, though it would not have been their actions that caused the raiders' retreat.
How do the raiders arrive without being spotted by satellite, radar, or coast guard? This shouldn't be a problem with their level of technology, but if you haven't thought of it, you should jot a note down somewhere.
How long is this battle going to last? You said to assume something like the US as the defenders; except for a communication blackout, it only takes fifteen minutes (at DEFCON 5) to scramble jets from QRA areas like DC and Norad. Other areas would take a little longer to scramble, but it isn't going to take hours and hours. That doesn't account for any planes already in the air. Most major metropolitan areas have nearby air support, possibly even from carriers if they happen to be around. I'd guess the defenders could have air support before the battle you outlined would end. That could actually serve as a decent reason for the raiders to withdraw, depending on their air superiority powers vs whatever jet force is inbound, but could also complicate their extraction exponentially.
Now, after reading all that, please don't take me to be a meanie trying to destroy your story or be negative or critical or whatever. Everything I've outlined is only how I see it and subject to plenty of mitigating factors. With the tech level these guys have, maybe they jammed communications. Maybe the defenders have a chance because the raiders' orders include preventing any prolonged visual contact at all (to preserve secrecy of tech and tactics), thus forcing them out of any real fight and drastically reducing the options for their air power to offer support. Etc etc.
As for actual tactics, here are some
this "armchair" general came up with, from your battle outline.
1) If the raiders are so keen on preventing any of their casualties from being recovered by defenders, the defenders can take advantage of that. Overwhelm a distant raider squad or fire team and prepare an ambush for the raider drones coming to dispose of the bodies. Focus the defender's anti-air at that spot to knock out the drones.
This works because it takes observed behavior (raiders don't leave any scrap of their presence behind) and puts that raider objective at odds with whatever other objective the raiders have, which the defenders probably can only guess at. The raiders are forced into an extended, open confrontation against the defenders who are entrenching themselves around the fallen raider squad, or else the raiders must abandon the fallen. This creates an advantage for the defenders and pulls raiders out of their careful defensive retreat.
The defenders can even pretend to salvage a raider intact and then demand the raiders leave in exchange for recovering the body. The raiders may be forced to attack the defenders' position to confirm or deny whether the defenders really do have an intact body, or the raiders may be forced to parlay. Either could be advantageous to the defenders.
2) If the raiders are observed taking captives, the defenders can deny them this possibility. This is obviously dependent on the ruthlessness of the defenders, but they can deliberately kill their own civilians who are captured. If the raiders' mission depended on this, they are now frustrated.
This can be mitigated by the raiders if the hostages are protected inside their vehicles, though that can backfire if the defenders focus on the vehicles anyway, possibly without even knowing their own civilians are inside.
3) If the raiders are relying on anything in the city, the defenders can deny them that. Destroying their own bridges, blocking roads, etc. This may not work if the raiders' superior mobility negates it; something you'll have to consider.
4) Interstates work well for moving tanks. In an attack, most civilians will flee away from the city; this should make roads temporarily clear going into town (I say temporarily as civilians will soon overflow into those roads, too). Depending on the military installation in question, there will be some tanks/vehicles on base/post; these could be moved to the rear of the raiders' formation, as judged by where the raiders are slowly retreating to. This would be far easier than moving them through the city itself.
5) If the enemy is observed to retreat from any serious engagement, the defending commander can take advantage of that. Either guessing or after careful observation, he/she can attempt to determine what is "serious" enough to make the raiders retreat, then fake it.
If it is just numbers, a mass charge may be called for. Or faking numbers, for instance with military personnel "drafting" willing civilians and having them march alongside real units to appear more numerous than their real fighting abilities would be. Particularly viable if the defenders are not all in uniforms anyway. In the US, this is particularly viable as there are enough guns in almost any city to fake an impromptu army, either from private stocks or taken from stores.
If it is support, using the limited number of tanks and helicopters available to threaten the largest number of raider positions could make the raiders fall back faster than actually committing these resources against one specific raider position. The threat of force can be quite powerful all by itself.
6) If the defenders figure out who the raiders are during the battle, they can claim to order retaliatory strikes on the raiders point of origin. This may encourage a withdrawal of raider forces. Obviously impossible if the defenders don't know where the raiders came from.
Against any nation like the US, the raiders will need some way to escape satellite detection, because after a raid this significant, every satellite available will be tracking them as they retreat. That means the defenders would know where the raiders retreat to. For reference, the EU, China, and Russia all have their own satellite networks online or coming up in the next few years, ending the possibility of sabotaging the entire global network by targeting/hacking a single nation, and you can bet every nation would track these raiders, whether they are friendly with the nation under attack or not.
Thus the threat of that tracking could necessitate a raider retreat, as the longer the battle lasts, the more satellites will be in position and watching. Even if they can't track the raiders' withdrawal, simply observing their capabilities will be a large intelligence boon against the raiders (who won't let their own dead fall into enemy hands for fear of the intelligence gathered from the bodies).
Sorry this post is so long.