What to do with some good links I have?

[Svetoslav]

I have some pretty strong links from relevant sources linking to the homepage of a site I deal with.

The links are usually from a PR3-5 pages and display specific result about the linking site. Sometimes they come from badges. We offer several services, so sometimes the page is about one service and next time about the other. Currently all of my pages link to the homepage. Would it not be better to link to the specific product page related to the page I have? Also I can do a canonical to the service pages?

Which would be best?

[RyanKent]

Would it not be better to link to the specific product page related to the page I have?

I would recommend linking to the most relevant page. If your site is about web design and you have a badge promoting web design, then linking to your home page is fine. If the badge is about graphics design, then you can link to your graphics design page instead of your home page.

Your SEO factors will be best served if you sincerely try to help users find information they are seeking.

Also I can do a canonical to the service pages?

Canonicals are used when you have multiple pages sharing the same information but presented in a different format. It sounds like these services pages display different information, so a canonical tag should not be used. It is ok to have some overlap between pages.