TL-DR:
If possible, convert your SVG to PDF (or eps) in Inkscape, then open that in GIMP and convert to a very high-resolution PNG without anti-alias (prints better), then embed that in your document. Because vector graphics support is a nightmare.
The long story:
Vector graphics support in Libreoffice is a very lively story ... at the time this question was asked, the only reliably supported format was eps. However, Libreoffice could not display it properly, only print to postscript printers (most network printers in professional environments) and convert to PDF!
The reason is that eps is already a postscript format, and the PDF conversion was based on "printing" to a Postscript file, then converting to PDF. Libreoffice simply passed the EPS images through, and in print they looked exactly as they should, although LO could only display a low-res preview.
A little later, around 2012, Libreoffice was, for a short time, able to correctly dspay and print SVG graphics! This relied on an installation of Inkscape on the same machine (or at least the cairo library that comes with it). The feature included all the fancy SVG features like transparency, gradients and blur(!). I used this to great effect in one single presentation in early 2013, and at that point I thought I had it all figured out.
At that point, someone in the LO community started thinking that "SVG embedding" is the same as "SVG import", and so, when inserting an SVG, Libreoffice started trying to interpret the file and convert it to a libreoffice drawing. That cannot work if the svg uses blur, for example, but in practice it also failed in lots of other scenarios, and this ruined several of my documents.
By now, Libreoffice has developed still a bit further, and at least simple svg images work nicely again. So as long as you have no gradients, transparency or blur, you should be fine with SVG. At the same time, something has happened to the EPS embedding, and they have started to look wrong in some cases.
Finally, there are more vector formats, like WMF and EMF. They can work nicely, but only if your document stays on the same computer. I've had several documents where fonts embedded in an EMF were completely mangled (or not), depending on what machine you were looking at the image.
... needless to say, I find this deeply frustrating, but it's still much better than Microsoft Office. To my knowledge, no vector graphics formats work on MS office at the moment (including Microsoft's own WMF and EMF), except the stuff you draw directly in the software, as it is for LO.
At this point, I've pretty much given up hope that SVG will ever be properly usable in anything but Inkscape itself and web browsers.
