I can't test this, but this and you didn't include your errored statement so I can only give you the tools to solve your problem. For reference, here is the documentation on the IF Function in SharePoint: http://office.microsoft.com/en-au/windows-sharepoint-services-help/if-function-HA001161010.aspx
In case that link ever dies in the future, here's the pertinant information for retentions sake:
Logical_test is any value or expression that can be evaluated to TRUE or FALSE. For example, [Quarter1]=100 is a logical expression;
if the value in one row of the column, [Quarter1], is equal to 100,
the expression evaluates to TRUE. Otherwise, the expression evaluates
to FALSE. This argument can use any comparison calculation operator.
Value_if_true is the value that is returned if logical_test is TRUE. For example, if this argument is the text string "Within budget"
and the logical_test argument evaluates to TRUE, then the IF function
displays the text "Within budget". If logical_test is TRUE and
value_if_true is blank, this argument returns 0 (zero). To display the
word TRUE, use the logical value TRUE for this argument. Value_if_true
can be another formula.
Value_if_false is the value that is returned if logical_test is FALSE. For example, if this argument is the text string "Over
budget" and the logical_test argument evaluates to FALSE, then the IF
function displays the text "Over budget". If logical_test is FALSE and
value_if_false is omitted, (that is, after value_if_true, there is no
comma), then the logical value FALSE is returned. If logical_test is
FALSE and value_if_false is blank (that is, after value_if_true, there
is a comma followed by the closing parenthesis), then the value 0
(zero) is returned. Value_if_false can be another formula.
Note this line, it will help you to understand the code example below:
Value_if_false can be another formula.
In our case we're testing if something is true, if it isn't then we need to perform another test. We keep doing these tests until no more options are available. In your case, your statement will look something like the following once complete:
=IF([Assigned Risk Value]="low",.25,
IF([Assigned Risk Value]="moderate",.5,
IF([Assigned Risk Value]="high",.75,
IF([Assigned Risk Value]="critical",1,
IF([Assigned Risk Value]="remote",0, "Unknown"))))) * [LOE #]
Basically, we're doing a test, if the value isn't true, we run another test, and so on and so forth. If you try this and you still receive an error please post the details here and I'll check back for you!