You bet. You can rollover multiple old and “orphan” retirement plans (e.g. Roth IRA, Rollover IRA, SEP-IRA, SIMPLE IRA, Traditional IRA, etc.) into your Self-Directed IRA. You also have the option to rollover funds in part or full in your old accounts into your Self-Directed IRA. And, yes, you maintain the same tax-deferred status within the Self-Directed IRA.
Traditional and Roth dollars must remain separate.
If you still work at your current employer, you could be barred from rolling your 401(k) over unless your plan specifically allows for it. You can check here for more information.
You can review the IRS Rollover Chart to see what accounts can be rolled over into other accounts.