Looking For App Equivalent

You could install MyPhoneExplorer (MPE) on your PC and phone. It's free. I haven't used it in many years so I don't know if it has a setting to launch and sync automatically when you connect to your LAN. But if not, you can use an automation app, like Llama (free) or Tasker to launch it whenever you connect to the LAN. All three of the aforementioned apps are well-established, popular, and (AFAIK) trustworthy.

I don't use this type of PC-software + phone-software solution anymore because cloud storage accounts are a better solution for me. I keep my files on (free) cloud storage accounts. That way everything is always synced between all of my PCs and devices, regardless of whether or not I connect to my PC's LAN. That doesn't necessarily bring your files over to your PC for offline consumption though. However, apps like Autosync (freemium) provide a variety of options enabling you to define sync parameters, e.g. only when on WiFi, only below a certain size, etc.

I don't know about Blackberry, but in general, Google wants you to adopt (and therefore makes it easiest to adopt) all of Google's services using their cloud based servers (Google Drive, Picassa-photos, Gmail-email, Gmail-calendar, Gmail-tasks, Gmail-contacts, Google Docs, Google/Waze-maps-and-GPS, Play Music, Chrome-bookmarks, Keep, etc.) such that all of your stuff is synced to all of your devices through Google's cloud. (And so that they know every freaking thing about you so that they can target you with ads.) It's convenient for Android users to adopt their set of solutions, and it's good for Google because it helps make you a stickier customer. But to Google's credit, they don't force you to live in their sandbox, just because you bought an Android device.

Check out Syncthing or BTSync. They will do what you want to do.

Logan382 said:

On the topic of cloud storage, does OneDrive have an offline mode on android similar to their desktop application?

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I always use OneDrive online (and I don't use the OneDrive app because I use the file-manager app-- Xplore), but it seems that you can make OneDrive files available offline using the OneDrive app. However, if you edit those files offline, apparently it won't sync, it will place the newer version on the server, labeled as such.