Since the enemy teleported their MCVs to a random location around the map, finding their exact location is a must. Use scout units to find their position.The moving patterns of the enemy units may also give you a good guess of where they are.
The enemy will dispatch Engineers everywhere to grab Tech structres around your position. Capture as much as you can, especially 4 Tech HMG Tower surrounding your base, as they will come in handy in stemming the tide of enemy infantry units early on, and 2 Tech Protector near your base to boost your defense capabilities. However, avoid being too greedy, otherwise low power will clap you hard.
Near your base, there are 2 Tech Concrete Fortresses, which is perfect for holding the enemy back. However, don't sleep on them, the AIs will quickly find a way to counter them.
The Tech Twister is the main feature to watch out for; while predictable, it can greatly affect your ability to build your strike forces. The pattern is always the same; Tech Level 10 is the first to be disabled, while the last is Tech Level 1. This also applies to the Tech Twister undoing the changes, but this is only temporary. Once the Tech Twister is online, do not expect to have permanent Tier 3/Tier 2 for the rest of the challenge.
Speed is essential, because Tech Twister hit at the 20-minute mark. Rush through tech tiers quickly and build an adequate army of high-tier units before the nasty Tech Twister hit. Then, if you are confident enough, try to rush and take out an enemy early on. Otherwise, defend and wait until you have a sufficient army to engage.
No matter where they teleported, each enemy base will have 2 Tech Nuclear Plant. European Alliance's base will always have 2 Tech Deposit Bank and 1 Tech Defense Bureau, while Pacific Front's and United States' will have 1 Tech Heavy Machinery and 1 Tech Maintenance Facility each.
Unless you have plenty of anti-air to deal with these strikes, it is not advised to go for an armor blob assault. AI ally's base can handle such strikes well, so let them deal with them while you go for a naval/air assault, which is one of the best ways to complete this challenge. Always avoid the blue smoke signals! Lionheart's strikes are devastating, and can ruin your hard-earned army. These Lionheart Strikes are summoned through their Tech Centers, destroying these or powering down their base will prevent them from using these support powers.
This challenge might be the only one where a partner AI fares the best. Since the enemy bases are at random, quite undefended locations, your partner AI can rush towards them and take out one opponent early on, at least on Easy and Medium. On Hard, count on them as a meat shield only.
If you decide to fight fair and square, 
China can be a solid choice. Centurion Siege Crawler with Yunru and 2 Eradicators can absolutely wreck enemy bases, while Nuwa Cannons and Sentinels can provide necessary support. More importantly, Qilin Tanks and Halftracks can hold up well when Tech Twister hit. 
Russia can also be chosen, with their versatile arsenal.
MCVs Rush (spoilers, but you know it already :v)[]
Now, if you decide to play dirty, then welcome, you come to the right place. Call one of your buddies for this strat. When the game begin, move your MCV immeadiately to one enemy base, while your friend move theirs to another. (knowing the enemies' position is critical here, as such, maybe one of you should delay the move and instead pop a Barrack up to get some scout units). Deploy your MCV between the 2 Tech HMG Tower and the Tech Protector, then immeadiately build a Barrack. Deploy your infantry and turrets to kill any enemy units that is foolish enough to attack, while your Engineers capture the enemy buildings and MCV. If everything goes smoothly, boom, congratulations, you had essentially took out 2 enemy bases. From then, build up and deal with the last base.