Before deciding not to do a 301 redirect you may want to check how much traffic volume you get from these pages. If it's not significant and for some reason you're unwilling to do a 301 redirect, I would suggest trying to get the actual links going to those pages changed to your new events page. Also you should submit your new events page to those who linked to your old events page to see if you can get link equity flowing to your new page.

I wouldn't recommend this approach. You definitely won't get penalized but you'll hurt your domain authority.

Subdomains are treated by Google as different websites (here's a great Whiteboard Friday about it) so by creating a subdomain instead of a folder you're diluting your "potential".

The better approach for your situation is create folders with geo specific locations and high performing/volume keywords. An example of this would be www.domainname.com/city-stateabbreviation-keyword (http://bestdefensega.com/woodstock-ga-lawyers or better yet use more "intent specific" long-tailed keywords like http://bestdefensega.com/woodstock-ga-lawyer-services )

This way when your geo specific pages get recognition from Google (whether through user data, link equity, etc.) it's not being diluted, it's full "potential" is given to your root domain which will help boost all of your pages.

Hopefully this helps!

-Jacob

The first thing that comes to my mind is "How much link equity do these pages bring in?". I know we SEO people hate to throw away any kind of link equity but at the end of the day we're not here to make SEO awesome for it's sake alone. We want results! We want to drive those heavenly KPI's we look at everyday. If these pages have really been a thorn in your side and are taking up your time I would suggest analyzing how much you'd lose if you just left these pages out of your new domain. I'd probably just cut them loose and make your life simple. If they're worth it though do the 301 redirect and see what kind of link equity you can get passed on.

Another option is just change the source link, if you can get in contact with the website that's linking and let them know what's going on that might be a good option. That being said these events are forever old so it might be met with a "That's not worth our time, besides the event is already past." when you ask for them to be changed.

Again I think unless these pages are bringing in some great link equity vital to your website to rank for keywords that are driving results... forget about them and spend your time working on something more valuable.

-Jacob

Like mentioned before these are organic sitelinks. They're generated automatically (as long as you have a functioning sitemap) by Google's algorithm when they feel there's additional content (beyond the main page that's returned) that would help the user find what they're looking for (here's the Google support article on it).

In your websites Webmaster Tools you can demote pages (this tells Google that you don't want that page to show as a sitelink) this doesn't last forever and isn't a sure way to control how your sitelink look.

Here's an additional article that gives you pretty clear steps to what I explained above (link).

I believe Yoast Plugin helps you create an XML sitemap so in a way, yes, Yoast Plugin can help you create sitelinks but it won't give you "complete control" at what those links look like.