UDP/TCP packet flooding router's firewall

[xauth]

In hopes someone can help me with this as nobody else seems to have the answer elsewhere that I've tried-

My problem here is that I get a load of UDP/TCP packets being blocked and some getting through from locations all over.

When tracing the IPs of the senders it's from all different locations, different IPs, while some being the same. This is happening even when no main computers are online, however much less (tested using LiveCD on laptop to view router settings.)
I'm not entirely sure if this is supposed to be normal, but the packet floods seem to slow down dramatically then when our main computers are off, but they still are present, even when the only thing open is just the web browser with the router settings/firewall log on.

The main reason this is a problem is because of constant lagspikes when games are being played as well as slow connection speeds randomly when these packets get blocked or get through.

Not sure if anyone here can explain this as I'm clueless as to what this could possibly mean.

Thanks!