Hangouts allows you to chat with other Google users if you know their email address. Hangouts can also be used for your text messaging needs if you set it as your default text messaging app.
Voice is Google's re-branding of GrandCentral. You get a phone number from Google, you link it to any phone numbers you want to link it to. When someone calls your Voice number, it rings all the other phones. It can also be used for text messaging. The text messaging capability can also be linked back to Hangouts, by default it's managed through the Voice app.
Hangouts Dialer is used in conjunction with Hangouts. You can use it to make IP-based phone calls, even if you don't have a Voice number.