Unless you give a user sudo access, you will have quite a hard time doing anything without a root user!
Assuming you haven't locked yourself out of the root account completely, you could use 'su' on its own to try switching to it.
Failing that, you could try logging into your linode using lish (the ssh console in the account panel). Even if you disabled root for ssh, console usually still has access.
If you still can't get anywhere, the linode panel lets you reset your root password through its web panel.
And finally, linode has a recovery image you can mount which lets you modify the linode from it, without actually booting it, although by this point its usually easier to start from scratch

.
Edit: about the spikes...
The linode graphs try to use the best scale to represent the amount of data/cpu/io your using. Your linode can use up to 400% cpu (4 cores), yet if you never go above 5% you will generally get a graph showing quite a bit of fluctuation between 2-4%. So seeing alot of spikes or large blocks isn't bad. As long as your not constantly burning through resources at a rate that would pass your cap or be unfair it isn't a problem.
(A Linode 512 host has at most 40 other hosts. A linode host has 8 cores. 800/40 = 20. If your
averaging over 20% CPU usage your eating up more than your fair share :p)