These connections come from robot spiders or bot nets. E.g. rough robots not following the convention of robots.txt, or bot nets anyhow giving a toss.
If they come from bot nets the machines trying to connect have been hacked / infested with malware, and are now used to distribute spam, recruit more machines into the bot net, set up SEO, or whatever else the herder (bot net "owner") wants them to do, e.g. run a DDoS attack or spy on users. "Good" bot net malware can be updated remotely by the herder to repurpose it to whatever pervert task the herder wants it to do.
Connections coming in groups of three can have several reasons. E.g. simply a bug in the malware, or a deliberate attempt to circumvent firewalls. I.e. many admins block IP addresses from certain countries like Russia, Germany or China, or even whole regions like all of Eastern Europe or Middle and South America. Trying from several machines increases the odds of getting through.
You see so many weird domain names, because there are so many weird domains out there on the Internet.